You appear to have attended to the single most important item needed to ensure proper operation of your mobile antenna. Here are a few suggestions regarding grounding:
1. Use the heaviest ground strap that you can find; I use 1/2" braid with eyelets soldered on the ends. I am told that copper strapping is better.
2. Solder all connections (i.e. eyelets) to reduce the possibility of future problems.
3. Use a dremel power tool or whatever to remove all paint from around the hole that you are going to screw the ground strap eyelet into. It MUST be shiny bare metal. The contact via the screw threads alone is probably alright but I always like to be 100% sure and I believed it might be insufficient.
4. Ground everything together that you can... i.e. on my 2000 Windstar I have grounded the rear hatch to the frame, the bumper mount to the frame, etc. This will not only help reduce RFI but will, for whatever reason, make the antenna work better.
5. GROUND THE ANTENNA MOUNT TO THE FRAME OF THE CAR. Unless you are absolutely positively certain that your antenna mount/base are grounded 100% to the vehicle frame, then for the sake of certainty, run a HEAVY ground braid from the antenna mount to the frame of the car. On my installation, although it looks strange as hell, I have a SHORT and very heavy ground strap running from my antenna mount to the frame of the car, in parallel with the mount, but to a different spot on the frame. (I cleaned the surface and soldered the eyelets). Pre-ground strap I was unable to tune the antenna on all bands, post-ground strap the antenna worked amazingly well.
6. Ground the rig! I ran a 1/2" ground strap from the rig to the frame.
Although I am not familiar with your particular antenna or mounting hardware, I am using a High Sierra HS-1500 screwdriver antenna and will shortly have all of my other antennas up for sale on eBay, including my Hustlers, helical whips and maybe even my AH-4 autotuner and whip. The HS-1500 didn't work worth a darn until I grounded the heck out of everything.
Oh, one other thing. Use the best SOLID DIELECTRIC coax that you can find. Does not have to be the heavy stuff like RG-213 or the like.... RG-58 will do fine for a short length. But use SOLID dielectric, as the foam stuff is sure to get scrunched at some point. And use quality connectors.... the BEST quality connectors that you can find. I used Amphenol with Amphenol adaptors and soldered all with a wee portable butane soldering iron/torch (takes a torch to heat up the shell for soldering outdoors).
There's a ton of other things that I could point out. Most are common sense. For example, I used those ferrite "donuts" on every power and control lead, both ends. I kept all power and control leads away from vehicle wiring and equipment. I used #8 wiring for my power leads, which are run directly to the battery and fused (both leads). Marine supply shops are the best source of mobile power accessories, such as wiring and fusing supplies. You should also pick up a couple of cans of LIQUID ELECTRICAL TAPE while at the marine supply.... it is wonderful stuff. I covered and coated all of my connections with it. The connections are all soldered as well. Then taped with high quality self-annealing tape. It forms a solid mass after a period of time.
Elsewhere in the forum you will see mention of a book by Don Johnson called Everything You Always Wanted to Know About Mobiling.... I highly recommend it.
In the end if you cannot get your antenna going, have a look at a "screwdriver" antenna. The DK made by Don Johnson is a good bet from what I hear. I chose the High Sierra HS-1500 by High Sierra Antennas (www.hsantenna.com
) for its quality and because it has a quick mount available for it (10 seconds to install/remover the antenna). Since I often park in Toronto, I often need to remove the antenna to prevent attracting attention to my vehicle.
Following all of the advice in Don's book and on this and other forums, my mobile system (IC706MkIIg + HS1500) has been an incredible performer and pleasure to use. I worked all continents in the first few hours on the air and have worked 50+ countries in the past four weeks. I cannot remember a mobile setup working this well in my 35 years of being a ham. I cannot say if it is the rig, the installation or the HS-1500 antenna, but I am enjoying being asked "you sure you're running mobile?".
Good luck. Please feel free to email should you think that I might be able to offer further assistance in any way.