cam choice for a fuel injected 340/416

Since you said you have a 340 stroker, you naturally have a hyd flat tappet engine. I would suggest to you to spend the money and retro fit it with a roller cam. It's going to be $1000 - 1500 to do so. Cam, lifters, pushrods, and an oil pump drive gear/shaft.

Either spend the money on roller or break in a flat tappet cam in that engine with a carburetor and then put the fuel injection stuff on. There is no time to play around with an engine with that many mods, retrofitted fuel injection, and a flat tappet cam and attempt a cam break-in. It can be done, but that is a tall order.

As for cam choice, you really need to be asking whomever is modifying the computer. They'd know what is and isn't too much cam. But I'd go with something in the 200 duration @ .050 range with no less than .500 lift. You could save some money on a roller cam by finding a stock roller cam and regrinding it, since youd need to spend money on custom pushrods anyways.

Good luck!