Is it genuinely too late to requeen this far north, or do I buy a mated queen and squeak it in?

Uppsala, third year, five hives. One colony has a queen I've been unhappy with all season — patchy pattern, colony never took off, wash numbers fine so it's not mites. I meant to requeen in July and life happened. My understanding of why it's late: raising their own is out because a new virgin would need to mate in September, and by then the drone congregation areas up here are basically empty — colonies have been evicting drones for weeks, and what's left flying is old. So the only real option is buying a mated, laying queen and introducing her now, this week. Is that still worth doing at 60°N in late August? She'd have maybe three or four weeks of laying to contribute to winter bees. Or is the boring right answer to let this queen limp through winter and requeen properly in May?