Isolating the feed line isn't your problem. It could be one of two things.
First, you don't have the antenna properly mounted. If there is a lot of metal around or near the antenna, you will not be able to tune it.
Secondly, the antenna is hollow. It is very easy to insert too much of the whip portion. This places the tail of the whip inside the coil making the antenna impossible to tune.
Here is a suggestion. Put the whip at its longest length. Use the analyzer to find the resonant frequency. It will be below 14.000 MHz, and may be as low as 13.500 MHz. As you slid in the whip little by little, if the resonant frequency suddenly goes down or haywire, you've got the whip too far in and you will have to trim it.
BTW, don't trust the 706's SWR readings, especially when the radio is warm. If you want more info on this, go to my web site and pull up the article Miniature Rigs.
PS: If an isolator cures your problem, then your antenna is not mounted correctly, in which case it will be even lossier than it is already.