Unfortunately whenever you try to lower either PH ar alkalinity both go down. The one thing I've read is to add an acid (PH down, muriatic acid (real nasty stuff) or even vinegar) in one spot without any circulation and it effects the alkalinity more than PH. I've never tried it but it might work.
My suggestion is to not worry about alk too much. It's only function is to lock in the PH so it doesn't bounce. If you have a Taylor kit and see what readings give you balanced water ... there are an aweful lot of "perfect" readings that can be had!
To get PH up get soda ash (I believe), there is something in the stores that'll raise only PH ... if it was a pool I'd suggest Borax but I don't know what effect (if any) it will have on your tub .. although I did use it once in a pinch ...
AND for baking soda, the heck with Arm and Hammer, buy generic ... I buy the store brand and get 2 lbs for $0.79 and it treats a lot of water ... both spa and pool.