This is not that far from doable. Your existing TBI will feed a 350 with a change to 350 injectors and a chip. Actually, if your not doing this for performance where you intend to run a lot of top end RPM you can get by with the existing injectors and just a chip.
There's a several ways you can go at this.
1) an entire 350 TBI injection, with wiring and computer from a wrecking yard.
2) a 350 computer from a wrecking yard, these should interchange with the 305 the difference being the part number of the chip rolls from the 305 to 350 with a different program this also changes the computer part number.
3) 350 injectors installed in your TBI to get the larger flow capacity the 350 requires. This gets into duty cycle. That's the time the injector is switched on compared to switched off. A 305 injector would have to be switched on longer than a 350 injector so a custom chip would be required to make this happen. The chip is a replacement for the one presently in your computer. The down side is that the 305 injectors are switched on for a longer period which causes them to run hotter, that can shorten their life span. The use of a 350 get around that problem. But there are people feeding 350s using a 305 TBI and injectors and I don't hear of any reduced life span for the injectors.
4) a custom chip for your existing computer, this can be for the 305 injectors on the 350 engine or a conversion to 350 injectors; some of these people can help.
If memory serves, NH along with most, if not all, New England states adapted California standards back in the early/mid 1990s. California law allows engine replacements as long as some guide lines are followed. Here's a JTR link on the subject:
What you propose is quite legal as long as you follow the receipe. Just refer to this as "an engine replacement" not "an engine swap" and you'll be fine.
Now I haven't checked to see if NH requires a trip through a techncial "referee" as does California. If not or even if so, I'll suggest that a 305 and 350 look the same from the outside. I wouldn't borrow problems by telling the state you took out the 305 and put in a 350 if you don't have to. With the smog gear hooked up and functional, these engines should look the same on a sniffer test. They don't test for absolute amount of exhaust product in cubic feet or pounds, they check for ratios of bad stuff (unburnt hydros, CO, NOx) to benign stuff like CO2 and H2O. So this engine replacement should work for you without any problems.