727 vs. 904???
Converters won't interchange. They are 904 or 727 specific.
Make sure the 727 trans isn't a lock-up converter type. A lock-up trans would have the splines machined at the tip that goes into the converter.
Chrysler did a lot of testing in the mid-'70's. They found that, built equally and with the same spec converter, a 904 was about .15 faster in the 1/4 mile than a 727. The reason being is that it has smaller, lighter components and a little less friction internally. But it may not be obvious with your set-up.
If getting it rebuilt, find someone familiar with performance applications, particularly Mopars. Not just any trans shop.
When I got my first car a looooong time ago, I went through 3 727's in a year with a basically stock 340. But I was abusing the heck out of it because I didn't know any better. Just a shift kit helped transmission life after that because there was less slippage and heat.
I have a 904 built by JW Transmissions in Rockledge, FL in my race car. Nothing trick, just a good, solid performance build. I believe the "red" clutches and/or bands are the better ones. I run easy mid-11's in the 1/4 with the wheels in the air every run, footbraking. Last trans was in for 4+ years and I had it redone just to be on the safe side. You shouldn't have any problems with a properly built and maintained trans in your application. An auxilary trans cooler and synthetic fluid always provides extra insurance. Synthetics reduce wear and hold up better against heat - the #1 cause of trans failures.