I would lean toward Tinker. You might want to consider how changing jobs at this point may affect your home purchase.
Honestly, in my simple young mind, I see it as a good thing as I will be making more money, and won't be losing anything in the terms of benefits. If anything I'll be gaining things. With my finances right now I can buy a house, but if something goes wrong, I'm screwed. That won't work. Working on base will give me breathing room and a little more financial security. However, being the new guy again and the unknowns with that are never fun to me.