Does the VX-6R allow you to go into AM mode on the frequencies you have static on? If so put it there and walk and wave it around the car watching the S-meter on the bottom, when it gets stronger pay attention to things 90 degrees from the antenna on the radio. It should help you locate if there's something loose in the 12v socket or if the spark plugs are the cause or a connection is bad somewhere or if there's just an on board computer or your ac fan putting out static. I once has some spark plugs that rust was forming between the plug and the cable, once I had a new distributor, wires and plugs, the noise floor was much lower on my car. Getting into radio you'll learn the value of good electrical connections.
Bluetooth and Satelite radio shouldn't interfere all that much. But I wouldn't say it's impossible. My experience has been they generally play pretty well compared to some other devices.
I'd also say verify it's not a range/dead spot issue, if you have a parking lot or street parking where these issues are occurring does it go away if you step outside the vehicle or are you out of range of the repeater or in the shadow of a building (or I suppose Noblesville does have a few small hills)? Do you have tinted windows? Some aftermarket tints have metal in the mixture, that can enhance the metal cage effect of the car.
Are the radios not transmitting or are they just no longer able to reach the repeater? If two radios are in the car can the one in the back seat not hear the one in the front seat with both on low power? (Usually takes a mobile radio but sometimes they can over load nearby radios and you miss that, and if it's not in repeater range I could see it seeming like it's not getting out at all).
A good mobile setup will pay dividends in signal range ability to participate and ultimately increased enjoyment of the hobby. I have a friend that the last time I rode with him he had a FT-1900 wedged between the seat and console of his explorer, attached to a thru glass antenna on the rear window (for the serious guys out there it was just making 2m rag chew easier when the cross band repeater was setup for the HTs or busy doubling as a scanner). They're also running $134 for the radio. I just pulled a FT7800 (old Yaesu ft7900 basically) out of my car; I used the remote head and separation kit (that was a freebie for the going deal at the time) and zip-tied the head to an OEM wire frame cupholder. The radio was bolted with the bracket it came with to the cover for the cabin air filter access, which if I didn't like the holes and wanted replacement runs about $70, but they're somewhere I don't have to see them and a little electrical tape and I don't hear the air pass through the holes with the radio out. So even if it's a lease or new car or small car, if you get creative (and make sure you attach securely in safe locations so in the event of airbag or accident nothing is breaking loose or at risk of beinglaunched into an occupant) you can find place to tuck things in. I found it helped to sit with the radio in the car for probably 20min trying different locations and methods before deciding where to install. I also had the head as part of the dash for a bit of time but attaching it to the bottom and keeping with no holes left the screen in a hard to read angle, but the install looked almost as though it was from the factory.
If you go with a mag mount antenna I'd suggest getting a NMO or SO239 mag base then an antenna to match up with it. Down the road should you decide to drill or put a lip mount on, you'll already have half of the equation accounted for with the antenna, and just be swapping out feed line. I also as part of the install I just removed, had the factory AM antenna removed, put a NMO mount in its place, put an SSB-2 there and it was actually shorter than the factory AM antenna and used the existing hole, no drilling required. Again keeping the look as factory-ish as possible, and not drawing excess attention from thieves. Heck most car club owners wouldn't catch it unless I told them, and other hams thought I just had the plates and no mobile rig. Best of all the FM antenna was integrated into the glass on a rear window so I didn't have to give up any music on that end (just the AM band coverage, but if I want to hear AM chatter I'll turn on an HF rig). I have an NMObase mag mount so when in other vehicles (YL's car for instance) with just my HT I can pull a corresponding NMO antenna and with a few adapters have great performance on the HT. Antennas before radios (google QRP DX to see what less than 5 watts can do with good antennae), but you'll likely see a big gain in radio performance going from 5 to 50 watts and a decent 1/4 or 1/2 wave antenna (avoid the little ones that are appealing by size and claim high gain, they are made to work with network of sites to support them). Don't forget to pick up an SWR tuner to make sure your antenna is setup properly.
Any notion or idea that may be in your head that an HT is all you need, you should take that idea and forget it. Seriously. Don't even think about it. 
