I would NOT consider this as a viable option. 305's already have a very low compression. And with a tired motor already, you'd be looking at a compression ratio at best in the low 7's and probably more like the upper 6's. You're 4.5hp Briggs and Straton lawn mower engine will have more power. (OK, a lil exaggeration, but not much)
As far as using 305 heads on a 350, depending on what type of improvement you're looking for, YES, a 305 head can certainly make an improvment to a 350. The 305 heads use a small combustion chamber so this will raise raise the compression ratio and give you more power. But, the 305 head runners are piss poor small so you will run out of air at low rpms. You could consider it a truck motor used for towing where all the power is at the bottom end and the top end just sucks and is gutless. I'd run a 350 with 305 heads and a 2bbl carb no problem and expect to be able to carry a good load and have fair mpg, but not expect any performance over 3800-4000 rpm.