Your main squeeze doesn't sound like a shrinking violet
I have HST on my Bobcat CT230 but it also requires setting the parking brake to leave the operator's seat while the engine is running, otherwise it does a forced shut down. Frankly, having a tractor that didn't require that would be an inherently unsafe condition. Don't bother looking for one unless you have an expensive insurance policy on your significant other that you're looking to collect on.
Anything in the 30 to 40 hp range sounds good to me for your needs. Get one with a cab though. Cab keeps your missus from looking like Frosty the Snowman's wife, and keeps crap that might be thrown up by the flail mower off you and her. And yeah, I know, a cab would probably keep you from parking it in your garage. There are tradeoffs for everything.
Hmm, my 3120 does not do this. I can start it up and leave the seat without putting the parking break on and it doesn't shut down. I don't find it as a safety hazard, more a idiot hazard. When the PTO is on is a different story though, shuts down right away. My lawn tractor (JD 345) shuts down when I get off and my 5410 (85HP shuttle). I really don't see much hazard in this though. The HST slows everything down, so even if it does start to roll, its not going fast.