Jon, its still prime mating season. If your hive has open brood (aka wet brood, aka eggs and larvae) and 2 frames of bees then it will reQueen in 16 days (probably less as they often take eggs that are 2-3 days old). In 10 days check hive to see if there are capped Queen cells. Then a month from today you should have a laying Queen. The upside to reQueening now is 1) no new brood for nurse bees to take care of so more of them are converted to foragers and you should get HIGHER honey yield 2) It forces hive into brood break - breaking up cycle of mite reproduction and lowering mite rates without any chemicals 3) Newly mated Queen most likely won't swarm this season but next year.
If you don't see laying Queen in a month and you have a second hive then you can put a frame of open brood and try again as long as you have enough nurse bees.