the only way you can really adjust the thermostat sensitivity on those particular systems is to in fact buy a new thermostat. You can possibly move the location of the thermostat bulb (usually located on top of the heater manifold) and put it into a drywell in the plumbing but that will most likely not give you more than a little bit more accuracy than you already have. check the thermostat bulb in its current location and make sure it is completely covered by the insulated plate on the heater manifold. Otherwise I would suggest simply replacing the entire thermostat itself, you may even want to consider getting a topside upgrade. The Ap-4 unit was usually made with a black 6 prong plug in the bottom right hand corner, if you have this plug you install a topside that has LED indicators and more importantly a thermostat control which you can place on the top of the spa so that you do not need to crawl under it to change the temperature. Here are some links to thermostat you may require and the topside you may want to consider.
http://spapartsnet.com/cgi-bin/cs/index ... d=ELB2TSTD
http://spapartsnet.com/cgi-bin/cs/index ... d=EXSPT430