Will your bees attempt to swarm in May

[Jambo]

Doubtful they will be naturally swarmy genetically from C4U.
Another part of the swarming equation is room. Bees need plenty of it, particularly early season when their numbers are increasing fast. I think it's reckoned that one frame of brood when emerged has enough bees to cover three frames, so easy to see how this can soon get them crowded.
If the queen runs out of laying room this can also cause issues.

Yes nail on the head there I think - they are prolific and I need to get more proactive on the laying room. They did both have double brood boxes laid wall to wall when they started on the QCs!

Drawn comb is a limiting factor for me as a new beek but I will follow C4Us advice published elsewhere to make a supply of that this autumn

That plus a ready supply of mated queens in early May....