Help with brassocattleya/epicattleya (?) - flower sheaths, when to repot

[adam123]

Hi everyone,
I'm sorry if this post isn't in the right place on the forum… Given that I don't even really know what kind of orchid this is, I thought it best to consider it as part of the Cattleya alliance and post here!
First of all, I'd really like some help with identifying this orchid. I've been doing a lot of research online, and come to the conclusion that it's probably a Brassocattleya Makai Mayumi, but I'm really not sure. I've also seen similar plants called Epicattleya and more recently, Brassanthe (or thereabouts…). Knowing exactly what it is will really help with understanding my orchid's needs.
I bought it a about a year and a half ago in flower, and it has since done rather well… It's kept in a very bright position (hanging under a skylight), but with very little direct sunlight. Since I got it, it has grown at least another 20 pseudobulbs which are just maturing now, and is sending up lots more. However, of all the new pseudobulbs, only 2 so far have sheaths… Could more grow on the maturing pseudobulbs or do they only come out as they grow?
I'd also really like to see this plant flower (nothing surprising there, I hear you say…)… But I'm not really sure of how to go about it! I know that sheaths don't necessarily mean flowers, so how can I encourage flowering? Does the plant require a temperature drop? More/less light? Big day/night differences?
I repotted when I first bought it as it was growing loads of roots outside the pot. I thought it would be OK for a while and that I could at least get it to flower once before repotting again. However, it has grown much more than I expected, and is starting to grow outside the pot again. I know that Cattleyas in general need a little time to readapt to a new pot, and I'm worried that if I repot now (even though the time seems right with all the new growths and roots), I'm going to miss out on flowers… What do you advise?
I'm sorry for asking these questions to which I could probably find the answers elsewhere, but without knowing exactly what plant this is, I'm in the dark!
Thanks in advance for your help!