You probably aren't aerating the tub enough to have the high TA raise the pH for you automatically via carbon dioxide outgassing. If you run the jets, then you can have the pH go up with no change in TA. You are right that the pH Up will increase the TA if you don't have enough aeration. By aerating more, you should be able to get to a point where the pH is more stable, though the TA might be around 150 ppm or so.
If you can't aerate, then another alternative is to use a pure base (i.e. lye) to raise the pH, but unfortunately there aren't any spa products I know of that use that. The next best thing would be to use 20 Mule Team Borax since that will raise the pH without increasing carbonates so raises the TA by half as much as pH Up. However, if you use that a lot, then you may add too many borates -- up to 50 ppm cumulative is OK.