Your vet is correct that your kiddo does indeed need his puppy boosters before you choose some sort of an adult vaccine schedule. After the boosters, rabies is then by law of your state, which you're saying allows 3 years - so after the booster you can then wait 3 years for the next rabies.
As far as dist/parvo - the compromise by the AAHA is that they should be given every 3 years, even though DOI is actually more thought to be around SEVEN years now.
Here is more detailed info and a schedule for vaccines:
http://www.yorkietalk.com/forums/yor...-overview.html