That's basically what's going on, the Jeep is small and since the top is fiberglass the only groundplane you have right under the antenna is the thin edge of the tailgate and tops of the rear quarterpanels. I've done dozens of installs in Jeeps many years ago and remember a ball mount on the rear quarter panel worked better than a spare tire mount but it was still troublesome.
As someone else mentioned, take some wire attached right to the grounded side of the antenna mount very close to the antenna and stretch it out sideways and see if that improves your match. You could try a 9ft wire or a couple of shorter ones, just make sure its right at the antenna base and goes out sideways from the antenna. If this gives you a good match then you know its purely a ground plane problem.
Grounding the mount to the chassis and other methods that do not provide a large surface of metal right at the antenna are not the same as having the antenna mounted on a large flat surface of metal. If lack of ground plane is your only problem you can fool the antenna by soldering a small value capacitor across the antenna mount from hot to ground. Try values from maybe 25pf to 100pf using a 100v or more rated disc ceramic or dipped silver mica and this will usually get the match in a reasonable range.
Another thing to look for is grab the coax with your hand and move your hand up and down the length of coax while measuring the SWR. If its stable then you have one less thing to worry about. If it changes noticeably then the lack of ground plane is forcing RF currents onto the braid of the coax and it will also radiate some. In this case you would need an RF choke in the coax and that's a separate topic.
prcguy
The Jeep is not big enough to provide a 'groundplane' at 27 mhz., or more correctly a counterpoise or other half of the antenna system.
Most use the 'no groundplane' Firestick antenna. Probably equivalent to a one half wave antenna.