This is what I do. I bulk prime the entire batch as though I'm bottling, bottle the few that I need, and put the rest in the keg. I then monitor the naturally carbing keg with a bleeder valve like this
. At room temperature, I know that I don't need to let the pressure go over 30 psi in the keg and I'll have nicely carbed beer in a few weeks. I realize this is an additional cost for you if you don't have the valve, but I use it on every naturally carbed keg I use, and never overcarb. This may not help you in the short term, however.
Your other option is to get some of those carbonation drops and use those in your bottles, and force carb the rest in the keg.