Yeah I put a cross batton between the beams actually but is that not likely to cause squeeking itself by shrinking/expanding?Every subfloor in my house will be 18mm ply by time I'm finished! If anything it's better.
On that bit shown open, I'd probably put a few cross battens if it was myself... not a lot of support there bar very thin edges!
You really want all 4 corners to be supported well so there is no flex.
Also, did you just drive in your ply with screws? I've got to get better screws as i broke two heads on my impact driver as they didn't get on well with the ply!
Any preference for type of screws?