I made a post about this a little while back which you can see
here. The short version is that I use a powered USB hub that runs off of a 5V input, combined with a first gen Modi, with my phone as the source. As mentioned by
@rkw a Modi 3 would actually make this setup even cleaner as you wouldn't need the USB hub for power. My only word of caution is that the strong output from a Modi (especially ones with a 2V output) might be too "hot" for some cars auxiliary inputs. It's not a problem in my Camry but it was in my partners VW Passat. So your mileage may vary.
I definitely agree that the upgrades you mentioned (new speakers, amps, subwoofers) are going to make a significantly bigger difference in your cars sound, but those components are also expensive, and either require you to know how to install them or pay even more to have them installed professionally. For what it's worth, adding the Modi made a noticeable improvement to the sound of my car which has a stock factory (aka trash) system. It's also just fun to put one in your car (for the nerd points).
I have looked extensively into upgrading my cars sound system, since I spend a lot of time driving and almost all of that time is spent listening to music. However, changing one component doesn't make much sense. Upgrading the speakers, the amplifier, and adding a subwoofer (the minimum work I would consider doing), with components of worthwhile quality, would cost about $1100. If I want other upgrades like sound dampening in the doors/floor or a new headunit as a source, the cost goes up from there. When the timing is right and I decide to make the upgrade, I will almost certainly look into moving to a Multibit DAC as the source.
To that end, I would also appreciate a link to a good quality 12V to 16V adapter that would work with a Mimby. I thought about this problem before and the only solution I came up with was using a
12V to 110V AC inverter plugged into the normal Mimby wall wart. This wouldn't be expensive but it would take up a ton of space.