investing in a good quality bandsaw instead. (Can you cut strips on a bandsaw? Seems like it'd be possible, as in some ways strips are a special case of re-sawing, which is one of the primary specialities of bandsaws, right?)

With a bandsaw there's no 'kickback' problem- that's one advantage.
Most small bandsaws are used to replace a hand power jigsaw (which used to be called a 'saber saw') cutting curves, or for rough cutting.
You need a pretty good (multiple $k) bandsaw to resaw well, though people do some amazing things with 14" bandsaws.
I have a good bandsaw and a Grizzly 14" and wouldn't cut strips with either- for starters there are no infeed and outfeed tables.
Without a tablesaw, I'd rip strips with a Skilsaw and a decent guide, though you need to think the process through in order to make ripping the whole board into strips easy. And, there's nothing to keep me from building one of those 'portable' 'table' saws into a bigger work surface.

I don't see the logic of buying one of those portable saws unless you have to wheel it out of the way to get the car into the garage, or you use it outdoors and store it in a shed. I think most small urban areas are like mine, and I can find used belt-driven tablesaws any time. Right now there are a half-dozen with cast iron tables and decent fences from $40 to $350 USD on the local online listings. None of them will tip over if you push a plank into the blade. You can always find a used motor for cheap.

But, I'm lucky - I got no arguments when I decided that the car wasn't going into the garage any more! :-)