Just checked - from what I can tell you still have to sign a paper at closing that says you will occupy the house for a year from closing but that works if your new closing is a year out - you could get a VA on your current house.
Here is what it says on the funding fee:
The VA funding fee is required by law. The fee, currently 2.15% on no down payment loans for a first-time use, is intended to enable the veteran who obtains a VA home loan to contribute toward the cost of this benefit, and thereby reduce the cost to taxpayers.
The funding fee for second time users who do not make a down payment is 3.3%. The idea of a higher fee for second time use is based on the fact that these veterans have already had a chance to use the benefit once, and also that prior users have had time to accumulate equity or save money towards a down payment.
I didn't dig deep enough to see what the satisfactory down payment is to avoid the increase to 3.3% - that is when you weigh FHA versus VA because you can get rid of the PMI.