I have people hunt blocks for me, I buy cores when they are available.
Nothing wrong with a Richmond 6 speed. But a 5 speed with a 3.08:1 gear is like a 4 speed with a 4.56:1 gear, in first gear, and a 3.08:1 gear in 5th. Somewhat cheaper and less complex. Either will be fine.
A well built 700R4 is a good option as well.
The 425HP 406 with a 700R4 is a common combination around here.
Have a driveshaft custom built. Although 55-64 Chevy rearends aren't the best, and aren't cheap, you can make one live behind a small block automatic setup easily, and it will do okay behind a stick if you are somewhat reasonable and prudent. The rest of the car should be fine. Beefing up the original will be about as cheap as buying something else and converting, with less hassle, and if you aren't going to race the car hard, it will live.
A convertible will be a little heavier than my old 409 hardtop was, about 150 pounds. I didn't do too much to that car, other than adding a second upper control arm on the rear, and stiffer bushings everywhere. The engine was STOCK. It originally came with two sets of head gaskets, and a set of different valve springs in the trunk. Took one set of gaskets out to raise compression, and swapped in the better valve springs. It was not too hard to maintain, despite solid lifters, dual carbs, and dual points. About an hour or so a week. I did kill a lot of Muncie 4 speeds, after I got the clutch setup figured out.
For your budget on the engine, you could get a REAL nice 406 with aluminum heads and a hydraulic roller, that will be reliable and low maintenance. EFI can be nice, but you better be able to maintain it or have someone who can. An aftermarket tuned port manifold with all the goodies, and a basicly stock GM system will run well. Or for a real nostalgia thrill, run two 350 TBI units on an Offy 2X4 intake. Done right, it looks like an old dual quad 283, and it is solid and simple.
The bigger the engine, the less stress it takes to make a given power level. That's why I like a 5.7" or 6" rod 406 so much. More power at a lower RPM than even a 383, and less trouble to build.
By all means, get a top quality coated header. And do not skimp on the exhaust.
Convert to power disc brakes. The brakes on that car SUCK. I know, I had a 409-425HP 64 Impala (wish i had it back, 6MPG and all), it would fly. But it wouldn't stop.
I do have a shop, have had for years. I do not have a website, I should though. I do build engines to ship all over, I have a couple in Norway, believe it or not. You can email me from the board if you want.