No problem... add a shift kit and a large trans cooler and it will be fine for your type of driving

 

I guess we're assuming the OP has an automatic trans, although he didn't say.
If so, you have to expect to rebuild/upgrade your 45 year old trans as you upgrade the engine. But, a properly upgraded TH350 trans will easily handle the demands you will be putting on it.
I have a TH350 trans in my car with a 383 with lots of 1/4 mile passes on it.
Regarding the radiator, I changed mine to a 4 core, L82 size copper/brass unit and i have no cooling problems.

 

Agree with Chili Pepper on the staged build. There is so much information on this site and many others about how to incrementally hot rod your 350 motor. However, have seen many builds be underwhelming due to mismatched combinations of parts. It all has to work together and is dependent on what you are targeting for hp/tq, rev range and power band, and objectives. Need something that screams to 7.5K, or will never see north of 5.5K? Want to mostly cruise or some track days as well? Good with a 14 second quarter mile or looking for mid 12s? Combination matching includes compression, heads (including cfm, spring rates, and rocker ratios) cam, carb, intake manifold, exhaust, rear gear, and torque converter stall.

Incremental builds are fun and easier on the wallet, but best to have in mind the end-state combination so it all works together to meet your particular objectives.

BTW. no one can really say that your tranny or rear end can't take the force of 33 more cubic inches without knowing the rest of these components (essentially how hot the build will be) and how you will drive it.

 

I am researching a 383 stroker and it seems that pretty much every single crate engine is based on the 1987 and up blocks with the dipstick on the passenger side. I guess the one upside is the 1-piece rear seal. Are there any compatibility concerns besides the dipstick side? Do pre-1986 heads still work?

 

I'm in the do it once and do it right camp. I wasn't happy until I was over 400HP, I would go with a roller cam 383 400+ HP from the start. You will be upgrading that L48 over and over. The trans is crap shoot, you will probably want at least a higher stall convertor. Cooling will need a upgrade, I'm running a 3 core champion that works fine. It's not going to be cheap, so set a realistic budget.

 

Then double it.

Seriously, sounds like you are going for a crate engine short block?. I have the post-1987 Gen I block for a 383 stroker in my C3. Built with an Eagle rotating assembly. Older heads will work, as will most everything else but the oil pan. I used the OEM roller lifter set up as those blocks have the holes for the lifter clamp vs retrofit roller lifters.

 

The difference in cost between building a 350 and a 383 is so minimal nowadays that it doesn't make sense to me to build a 350 anymore. I had an old school 383 (factory 400 crank) in my '79 for many years. It was an excellent performer but not so radical that I had transmission or cooling problems. Stick with a reasonable camshaft and compression, and don't drive like an idiot and you won't have any problems.
FWIW I went with w 427 small block after I broke the crank in the 383. I would never build a smaller engine again. The 427 makes huge power effortlessly. I could never go back. I guess displacement is a slippery slope.