Not an interesting idea at all. It is not possible to launch a missile vertically from a fixed wing airplane at proper speeds. This is the equivalent of attempting to close the convertible top of an E93 M3 while doing 250km/h on the Autobahn.
Those VLS micro-missiles would almost certainly be intended for large, slow, high-value assets like tankers, AWACS, transports and bombers etc. Although a case can be made to design a defensive UCAV around the VLS to fly escort rather than try and mass integrate the VLS across all those airframes, both for the sake of speed of introduction, as well as cost/performance penalties having them integrated would impose on all those assets.
Fighters like the J36 won’t have the room for them, and as you already pointed out, they would need to sacrifice most of its speed/energy advantage to use them.
If the J36 can mount DEW, it would make far more sense to just add a couple more arrays to give it full 360 coverage and use DEW for self defence. Indeed, DEW on the J36 would make far more sense as a defensive weapon instead of offensive, since you really wouldn’t want enemy assets to get close enough to your J36 to get within DEW range in the first place.