Beginner Road Racing: Transmission Question for Budget and Angry Knee

I admit I hesitate posting this thread since I see it quickly going off topic into a "manual rules" and "automatics rule" debate, but here it goes. My question is not of personal preference as much as practicality for two reasons I discuss below. I recently posted a question in the engine section about my interest in starting road racing at a local track, just against the clock for now. I recently purchased a solid but neglected unrestored 1969 Valiant coupe for the build. It’s a factory 318 4-speed car that doesn’t run but still has the engine and transmission. I'll run an LA for the weight and because I have LA parts to put together. I'm shooting for 400 - 450 HP at the flywheel. There's the general context.

For the transmission, is a 727 full manual shift valve body transmission with a custom converter built for the specific engine/car practical for road racing? Hear me out.

Point 1 - Budget:

This is a budget build, not as in unsafely hacked and cheap but as in economically reasonable. As my first step into the fray, I don't want to over-invest funds or overestimate my abilities as a driver.

Manual Transmission: Safety (even though racing is inherently risky) is a big consideration at this point in my life, so running a manual transmission will require I buy an SFI flywheel and scatter shield whether the engine's 400 - 450 HP needs them or not. That's just how it has to be for me if I put a manual in the car, which adds a considerable amount of money to the build even before rebuilding the transmission and buying a good clutch system. As far as a core goes, I have the A833 in the car, but it needs going through. Another option is to pull an NV3500HD from a junkyard Dakota, but I'm not sure its five speeds and ratios are the best for a road course with more tight turns than straightaways and sweeping turns, and it has a integral aluminum bellhousing, so I would need to either find a shield that fits over it or reinforce the body tunnel and floor with plate steel.

Automatic: On the other hand, I have an LA 727 in the parts shed that I rebuilt for another project that didn't get used. It has a Hughes manual shift valve body, 5-pack red frictions/steels, 4-pinion planetaries, oiling modifications, etc. I'd only need to buy a custom torque converter and a floor shifter to make it work. I'll be going to a larger drive shaft and U-joints regardless of the transmission, so that cost is already baked in regardless of the transmission type.

Point 2 - My Knee: Most of my commuter cars throughout my life have been manuals. I had a left leg injury years ago that tends to remind me if I overuse my knee in certain ways, and operating a clutch pedal and jumping to a brake pedal quickly is one of those ways. After a spirited 10-hour road trip that included some mountain roads, the manual commuter car got sold for an automatic. The knee otherwise works fine and is healthy according to the doc. I know for a fact that it is not going to like a few sessions of a full day at a road track pushing a strong clutch and brake pedal let alone doing that at least one track day a month, even if I set up a hydraulic system where the clutch feels like a modern pedal. I'm okay using the left leg for the brake pedal, but a clutch pedal added to the mix will likely make track days a lot less fun.
I admit I hesitate posting this thread since I see it quickly going off topic into a "manual rules" and "automatics rule" debate, but here it goes. My question is not of personal preference as much as practicality for two reasons I discuss below. I recently posted a question in the engine section about my interest in starting road racing at a local track, just against the clock for now. I recently purchased a solid but neglected unrestored 1969 Valiant coupe for the build. It’s a factory 318 4-speed car that doesn’t run but still has the engine and transmission. I'll run an LA for the weight and because I have LA parts to put together. I'm shooting for 400 - 450 HP at the flywheel. There's the general context.

My Concern about the Automatic: At the drag strip and on the road, I've never been in a situation where I'm going into a corner hot, braking hard, and downshifting a 727. My imagination sees locked up rear wheels, fishtailing, possible spinning, and eventually the smell of fried ATF/clutch. With a manual, I can double-clutch and/or slip the clutch to help ease into the lower gear, but with a 727 I have to leave it up to the transmission to a larger extent. How does one practically manually shift a vintage automatic at a road track? Does it require planning corner entries sooner to get the engine RPM down, or will downshifting from 3rd into 2nd not be an issue? I don't see needing to downshift into 1st at this track.

There you have it. I'm trying to deal with both budget and comfort/health when planning the transmission for this build. I appreciate any constructive feedback those with road track experience/knowledge can give about running an automatic in their vintage cars. I can't be the first. Thanks.