Steve Pierce of WSDOT was able to get back to me with more precise numbers about the STP and CMAQ funds that state and local government could shift to transit:
Washington state was apportioned $930 million of federal STP and CMAQ funds from 2007-2011. About 65% of these funds are sub-allocated to MPOs, i.e. PSRC. If the MPO selects and programs a transit project, the lead agency may request a transfer from FHWA to FTA to ensure the efficient delivery and transit expertise necessary to complete the project. At this time, there is no legislation limiting the amount of funds that can be transferred to FTA. The majority of the $104 million is associated with projects from the PSRC.
In other words, state and local government had the opportunity to divert a further $826m over 5 years from highways to transit. A chunk of that decisionmaking resides with our very own Puget Sound Regional Council.
To come back to my original point, to de facto fund transit with a state gas tax increase would require a bit of coordination between PSRC and the legislature, where PSRC agrees to shift funds to transit and Olympia decides to backfill the road projects with gas tax. But there is no constitutional barrier to doing so.
Note: the general question of whether transit should be subsidized is off-topic.