At first blush, you might think that the U.S. Supreme Court (not the States' courts, which have come up with some doozies in their time, like the one in Vermont which found that a beer-drinker parked in his own driveway was actually on the public highway for ethanol industry support purposes) would frown upon such restrictions of free interstate commerce.
Consider, for example, the SCOTUS rulings described in earlier columns in this space which required both wheat and marijuana grown for personal, intra-state consumption to be regulated just as if they were in inter-state trade; but then also consider the absence of a similar ruling regarding the presently-prohibited selling of health insurance across state lines, or the several never-challenged restrictions on interstate commerce involving a variety of internet-based sales, wine in particular.
New York State and New York City, a couple of decades back, had some special taxes for New Jersey and Connecticut commuters, and the court never blinked. I'd guess that the new court, with its new emphasis on empathy (particularly toward at-risk state budget goals) might turn a friendly judicial face to states seeking to discourage their more lucrative citizen/taxpayer profit-centers from departing.
SCOTUS itself has had some ideal-budget shortfalls and inflation-adjusted pay cuts in recent years, even before it became more group-identity empathic recently. If you're uncomfortable with the bluntness of the "exit fee" label, you might consider an alternative-such as negative impact fee.
Positive impact fees are already accepted governmental profit-centers in various jurisdictions across the country, billing new development based on estimates of the new costs it will generate for the taxpayers in existing development. A negative impact fee would cover the opposite calamity: taxpayers who abandon their rightful obligation and ungratefully flee. It should be argued that over the years, such undeservedly fortunate folks, who prospered under the aegis of a beneficial state government, didn't actually pay for all the goodies they got.