I think you are right, if the contact could be moved to the 'other side' of the coil it would probably tune just fine. As it is, it should get you 'close enough' for your radio to handle the mismatch. If not, then there are a couple of 'tricks' that can work for you. One of them if to use a short clamp-on wire attached to the whip above the coil. That wire/rod sticks out horizontally. It doesn't have to be very long at all, just a few inches, 4, maybe 6 inches long. It acts as a small top-hat, and could add enough "length" to the whip to find a usable tap point on your antenna. Of course, adding that wire/rod will change the tap-points for other bands, that's why it's removable.
I haven't owned an antenna like yours, but have used the same sort of thingy on another such antenna, it works.
Have fun.
- 'Doc