Welcome to the LowDown, Iffler. You'll like it here.
In your situation, you might rent a bass. Good way to start. I did a bluegrass tour in France in 1998, and they rented me a bass. Not too bad, as these things go.
Action affects tone tremendously. Unfortunately, the lower the action, the less punch and power the URB will produce. As said above, it begins to sound too much like an electric fretless. Might as well play one of those, if you get my drift.
Keep that beater you've been diddlin' with. Can you buy it? Get a competent luthier to check soundpost and placement, fix all cracks and buzzes and cut a new bridge with wheels in it. Get some good strings (for small hands, the Corelli Tungsten have a nice balance between punch and playability) and study properly with real technique. It'll be fun.
The URB is a different instrument than your electric. Technique, including fingering is very different. Use what you know as a springboard, but learn URB properly with a teacher.
For further information, do a search here. I've written extensively (usually, under my "davebrownbass" personality) about upright purchase suggestions, upright buyer's checklist, upright technique. You'll find a lot of useful info.
If you have other specific questions, feel free to ask.
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Yep. I'm the other voice in the head of davebrownbass.