So I have both a big block (1970) and small block (1973) Road Runner. I just built a stroker 340 that has 416 cubic inches for the 1973. It runs like a scared ape, but no, doing a build like that will not be a budget build. With aluminum heads and intake, it is a really light and powerful package, even in a big, heavy B-body. But the biggest cost is the stroker assembly (if you stick with stock heads). Once you get to machining, doing so for a big block vs. small block will be the same.
Having said that, swapping to a big block is NOT just some motor mounts. Don't forget about alternator, power steering, A/C and other brackets. There will be lots of small parts that will add up quickly that do not bolt between small block and big block engines.
Don't get me wrong, from a budget perspective I still think the best way for you to get some budget torque and power may be to do a mild 440 build, but just don't forget about the other stuff too. Another option is to buy a complete stroker 360 engine, for example from Blueprint engines. These can be quite reasonable in cost and drop right in.
Good luck with your project!