Warm Temp Keg Carbonation Problems

I just switched to a corny keg system and life is good. Well, sorta. My basement stays around 68-70 F year round, which is good for fermentation but bad for serving temperature. Alas, I do not have a beer fridge. So, to have the adequate amounts of CO2 at this temperature, I calculated something like 24-26 psi. Since I have a beer tap on a ball lock on my keg, I get a lot of foam. If I carbonate at 24 psi, then relieve the pressure prior to pouring, it comes out a little under-carbonate and then I have to top the keg off, using up more CO2 per keg than is necessary.

Can I resolve this problem using a picnic tap and 6-8 feet of tubing? What else can I do?

At that pressure you need more serving line (= greater pressure drop) to reduce foaming. I don't have the specs on hand, but google pressure drop per foot for the ID tubing you are using and divide your serving pressure by that amount to get your length.

When I do soda at 30 psi, I need nearly 25 feet of tubing to get a foam-free pour. If you get long tubing, like 20 feet or so, you should be foam-free at 70 degrees.