Hate to say it MountainmanPete buy I agree with the Vernal shuttle people.
Some big snow years like 2011 (2010 & 2014 were good too) the Yampa can run almost 2,000 cfs @Deerlodge on July 3. Last year was a decent snow year up north + late summer rains, so the Yampa@Deerlodge was ~1,800 cfs around July 3, plenty of water to float.
This year though, the snow pack looks a lot like 2012 so if I had to guess, plan on 200-500 cfs for early July, unless something dramatically changes before your launch date. If it were me I'd hold onto the permit and see how things look the last week of June. Maybe you can IK or self-support kayak if the flow is under 500cfs.