With a proper driver and fuel flowing through it those injectors can be held open for minutes at a time without overheating.
Yes, the crossfire setup can be bolted onto a 350, the '82 and '84 corvette used exactly the same setup on a 350. It will not bolt to vortec heads, they didn't have the same bolt locations and the intake ports are taller and won't seal properly. The '87 and up heads (pre vortec) have a different center bolt angle but same locations. You can get bushings to adapt them (some will slot the bolt holes but in this case you won't get away with it, you'll end up with a vacuum leak).
There are injectors available from somewhere in the mid 40's to 96pph (though bigger that the 72 or 75pph big block injectors are very hard to find in the correct configuration. OTOH, if you only need a little more flow than more fuel pressure will work well. The stock setup typically will run at 9-12psi, but most cars will run better with it boosted up to 12-15psi, and I've seen them run as high as 25-30psi (but remember that the flow increase by raising fuel pressure is only the square root of the pressure increase, it's not linear).
the stock fuel pressure regulator can be modified to be adjustable, but be aware that the stock plumbing with uses staggered injectors, they are not the same size front and back. If you upgrade and can't find a staggered set you'll have to replumb the fuel system, gutting the accumulator in the front injector tower and connecting the 2 injectors in parallel instead of series like stock. Also, you might find the stock pump doesn't want to deliver much past stock fuel flow, the easy solution for that is to run a later TPI style pump.
If you decide you need more airflow the TB's can be ported quite a bit, some stop at 2" bores, but its not hard to go past that. Injector tower spacers will also give you more airflow, and anything that raises the injectors higher will result in better fuel distribution.
If you start looking into reprogramming, yes, you can burn a new chip for the stock ECM, but you're better off converting to a later TBI ECM, like the 7747 truck ECM or even one of the aftermarket modified versions (do a search for EBL Locker).
I can keep going, but this is probably already getting overwhelming. The thing to remember with this setup is that it's all about monster torque. it will absolutely obliterate a comparable TPI setup WRT low end and MPG, and properly tuned will beat many much faster cars from a stop light, so if you're making changes take that into account. I had an '83 crossfire TA which with some work (but still the original 305 with something like 150K miles on it) that ran mid 13's at 100mph and got 35-37mpg on the highway. With 27" tall back tires I actually ran slower going from 3.23 to 3.42 rear gears (I blew up the stock gears and had a set of 3.42's sitting around).
In the first picture you can see the front injector tower modified to have a schrader valve so you can hook up a standard FI pressure gauge, the back FPR is modified to be adjustable, TB spacers under the throttle bodies, and injector tower spacers spacing the towers up
The second picture shows the bored TB and the spacer. The rest are just detail shots.