Well, tuning is the issue. Fueling is controlled by how long the injectors are commanded to be open, which is "hard coded" into the ECM for situations like cold engine, heavy engine load (hills, acceleration, etc). Whether the fuel pump is enough for the engines fuel demand is another story, but until tuning is done with the chip there is no way to know if the pump is capable of providing the amount of fuel necessary. More power=more fuel, the TBI pumps were marginal at best, but they would feed a stock 454 when operating properly (albeit with very little room to make more power) so they SHOULD feed even a moderately strong 350.
You can test fuel pressure via the free tool rental program at places like AutoZone (test at one of the joints along the frame rail). It *IS* common for these things to split the hose in the fuel tank (if it hasn't been replaced after the introduction of ethanol) which can lead to weird drivability issues. Fuel pressure test will eliminate that as a concern. I saw mine as an immediate bleed down of pressure to 0 as soon as the engine was turned off. But it also intermittently ran terrible under all conditions.
If it idles decent and isn't terrible driving on flat ground at moderate speeds (~35-50mph) out of overdrive, I'd be a bit surprised if there were any mechanical/parts issues.
You can try playing with the distributor (as long as you understand how to set TBI timing) to see if you can make things a bit better by adjusting the base timing, but you will run into knock before you can even hear it, and prolonged running like that is obviously not good. So even if you can make it better, it's not a solution. It's just another way to see if tuning would make the difference.
Regardless of whether the issue is singular or multiple, the thing needs a new chip burned. You just want to make sure it's running as good as it can when you have that done.
