Thanks for this and we love photos. Additionally, there are a few youtubes. Haven't rebuilt my 904 or 727 but have removed and installed them. Wish I had since I rebuilt the A-413 in my 1996 minivan which is the FWD version of the 904 (even termed "Torqueflite"). I agree that removal and installation is the hard part, and even more in a FWD, so why not try the "easy part" yourself.
I was first inspired by doing a forensic teardown of the original A-413 which had lost reverse. I found it much simpler inside than the cut-away drawings suggest. Turned out the problem was just a torn rubber lip on the L/R piston which I could have fixed from below. I had even removed the valve body searching for a problem, but didn't check that part and had to put it back before an out of town trip to move a kid to college, having to drive with no "R" (very careful to park gangsta-style on downhills). Surprisingly, I can get that lip seal and even a better aftermarket piston for my 904 and 727 but not for the A-413. Since that tranny case was cracked from a prior accident, I bought a used one. It had a rebuilder's label "Certified Transmission". After ~30K miles, the engine began flaring rpm on shifts so I took on rebuilding it, and had an extra vehicle then so no rush. I bought the Chrysler manual, which better than the ATSG one (just a copy) since also had info on upgrades and other tips. The manual is very step-step with a drawing for almost every step so it you follow it, almost impossible to mess up. I found the rebuilders had added an extra steel plate in one of the clutch packs. My only guess is they did that to re-use worn clutch plates. Now you know why most warrant their rebuilds for only 10K miles. A clutch plate costs all of $2. I bought better "racing" clutch plates w/ HEG friction (dark brown vs tan regular) for the wear-prone pack (L/R clutch I recall). I found those clutch plates in the OE tranny almost worn to bare steel, so little life left. Another oops by the rebuilders was that they left off the nut retainers on the output shaft which secures a set of tapered roller bearings (preload set by shim washers like in a differential). The nuts had loosened, which was the likely reason those bearings were pitted. I fussed over getting replacements ($65 ea dealer, 3 weeks) until I looked up the PN and found a common bearing set used on trailer axles, so bought the priciest ones at a local trailer supply ($6). The A-413 has the same/similar centrifugal governor on the transverse shaft (turns 180 deg thru bevel gears to the differential in FWD transaxle) as in a 904, a spring-loaded hydraulic valve (I think).
Had to go back into that transmission twice after that, both times because the L/R metal band cracked in two. Both times were when backing up my sloped driveway with a heavy load of lumber or blocks. It is cast-iron vs the spring steel of the front band. First time I thought a fluke, but after the second failure I researched. Turns out a common problem among Neon drag racers who turn up the pressure setting in the valve body. So, I loosened that spring setting. Wish I could have connected a pressure gage to do it right, but couldn't find a fitting for the little pressure test ports on the side. If you do adjust, very tedious since must drop the pan each time. The tip that a sedan transmission is that a spider gear has only 3 gears instead of 4, indeed Neon draggers prefer a spider from a minivan tranny. No broken band in >50K miles since the last replacement. If going in-there many times, consider a reusable silicone gasket from Real Gaskets of Tennessee, which I have on my 904 and 727.
Later, I rebuilt the A-604 in our 2002 T&C. It had shown no problems, but had to remove it to replace a cracked flexplate (common problem w/ larger 3.8L V-6) and since ~200K miles w/ no history I figured it needed it. I ended up just replacing the rubber since the clutch plates were only worn 1 mil (out of ~45 mil) so "like new". Went back in again 2 years ago at ~270K miles since a leak from apparently the front seal and found the plates still almost unworn, so doubt it had been rebuilt before we bought the van. I suspect the leak was actually coming from a crack at a torque converter bolt pads (didn't think to check that before shipping it back as a core). As stated, if going to the trouble of removing a tranny, not much more effort to go inside it. BTW, the A-604 is the one which started the "bad transmission" story in Chrysler minivans (V-6 engines since start, 4 cyl since ~2002). Actually it is a great tranny and all little glitches were fixed by 1989, I think the first without any bands (uses extra clutch packs to "ground planetaries to case), as most/all today use. Their first with electronic shift, using input and output speed sensors (no governor, solenoid pack on front). The reason they failed is that shops would refill with cheaper Dexron, pointing to a little note in the Owner's Manual that if ATF+3 fluid wasn't available, you could use Dexron in an emergency. That caused lockup chatter to wear out the torque converter plates. Shops still do that today, claiming "added a bottle of friction modifier". Did I say don't trust shops?
BTW, one tip is that people report fussing with pulling out the front oil pump. After you remove the bolts, there is just a circumferential square O-ring holding it in, which might have gone hard. Two bolt holes have larger threads to install puller bolts. I simply screw regular bolts in those holes and alternately tighten them, which pushes against the step behind and easily pushes the pump out. If the bolts mar the gasket behind, no problem since you will replace that. Haven't done that on my 904 or 727 but likely the same. Best thing you could have is a metal table with drain, like pro shops have. Even after draining oil, you would be amazed how much oil comes out of parts. Have a thick stack of newspapers and keep changing them as they soak up oil.
My only 727 rebuild experience was that in 2001 I had a rebuilt transmission (Oregon Transmissions, I recall) sitting in the garage to match a rebuilt 383 short-block. I was rushed to install them since I got a cross-country job offer and the moving van was coming soon to load my 1965 Chrysler. When I began to bolt them up, I found the transmission was wrong, for a later year. Indeed, I found my 1965 is a 1-year only (cable-shift w/ sliding yoke output). The shop doesn't have a book? So returned that one and had to get mine rebuilt locally in a few days. I asked at Aamco Transmissions, Buford Hwy in Atlanta and the manager said "nobody on staff who can rebuild a transmission" (not kidding, so what do they charge customer for?). Instead left it with Cottman Transmissions and let them know the main problem (morning sickness). Later, in California, it showed the same morning sickness (must idle 20 sec in "N" to refill torque converter before you get any drive). I since found an aftermarket valve body kit which is supposed to fix that. For all I know, Cottman just washed off the case and never even went inside. Took it to a Cottman in CA who said "we'll check it free". The "mechanic" showed me the oil pan with a piece of broken cork pan gasket and said in broken English "bad clutch plate". I told him B.S. and put it back together. They did, with the now torn gasket and refilled the same fluid they drained (probably dirty now), so I had to redo that. There were ~20 customer cars parked in front that I never saw change for a month as I drove by, likely held "hostage". Reported that shop to the CA BAR to investigate, and they disappeared within a year, likely to grift elsewhere. Did I suggest not trusting a shop, unless you get personal recommendations? No Yelp then, but shops game that anyway.