Brent--I have been an SWL since 1972 and a ham, off and on, since 1974. Since most people have space and aesthetic limitations, I agree that you should put up a decent ham antenna (say, an 80 meter inverted vee fed with coax, or a doublet fed with ladder line) and use it both for hamming and for SWLing. For decades, I was quite happy as an SWL with random length wire antennas--they're cheap and fun to make, work fine, and I got satisfaction from using a homebrew vs. commercial antenna. I use my ham radio antennas now for double duty, and they work fine. I absolutely think you do not need a dedicated SWL antenna in your situation.
Remember, unless you're chasing low power African, Asian, or Australian domestic short wave broadcasts, or unusual utility stations, most SW broadcasters have huge antennas and lots and lots of power. International short wave broadcasters have, relatively speaking, very strong signal strength. And, if you aren't picking up the BBC or Radio New Zealand International too well on the 31 meter broadcasting band, they often are broadcasting the same program on another band that you might be able to hear fine.
That's why less-than-ideal random length wires often work just fine when you're an SWL. I still have one up here, since I have an old Drake SW-4A in my sunroom and like to listen to broadcasts from there. If I'm in my shack, I have lots of other receivers and I use my inverted vees or inverted L for listening--whichever works best. But in my opinion, while a particular commercial antenna might work fine and be well built, the wire antenna you put up yourself in your backyard works just as well...and is a reaffirmation of and a nod to the rich tradition of homebrewing of antennas and radios and stuff from the good old days.
I strongly encourage you to build your own wire antenna! Good DXing, Tony