a chevy 350 is quite an upgrade from a chevy 305, for very little money.
You have the option of upgrading your 305, but that is like spraying febreez on crap... could work a little, but not worth it.
chevy 350s are EXTREMELY common, and you should be able to find a running one under $500. And even a rebuilt or mild performance one for around $1000.
Swapping engines is not much harder than upgrading parts on your 305, so why not go for it?
That being said... there are small things you can do to wake up your 305. Forexample, if you have a 2 barrel carburator, you can swap it out for a 4 barrel. Factory quadra-jet 4bbl carbs are great, and even competative with some high-end performance carbs.
There are many small tweeks you can perform to gain that extra bit of power...
can you add some pictures? People will be able to give advice paced on your current setup.