Bluetooth is finicky tech. I bet if you spend some time in the settings you can get it to connect the way you prefer. As long as the deck is halfway modern (not a 2008 implementation of bluetooth for example) I'd think it would support that.
Too bad about the sound quality being "okay." I'd expect more from JVC. Your comment on the "static" has me curious. Hopefully there are improvements to be had here. You'll have to keep us posted on that as you learn more.
One word of caution on remote starters. The only one I've personally worked with that's worth a damn is AstroStart, and you'll pay more for one of theirs. Most of the remote start units on the market require you to butcher the car's wiring pretty severely, and I just don't trust 'em. Not to mention our Marks have PATS (the chip-key) that has to be bypassed to make the remote start work. (or just tape a spare key under the dash..) Don't get me wrong - I live in Minnesota. Remote start is handy, but I've always opted not to put one in any of my Lincolns..