My best suggestion would've been to change the transparency, but this obviously doesn't work for you. Maybe @Shawn Wallwork or @Richard Leeke will have some ideas for you, as they are both good with maps. Otherwise, I would recommend placing this in the Ideas section of the Community!
It should be possible to do a dual axis map, drawing the state boundaries as a polygon on top of your current map. Out course that means that you have to find your own source of state boundary data. There is also some slightly ugly stuff that you would need to do to reshape your data to do that - and you will end up with a lot of nulls that you have to hide somewhere.
On my phone at the moment, will try to remember to dig you out an example when I get back online in a couple of days.