Can drywall cover a 30" span on the ceiling?
Opinion - you're nuts to bury those nice exposed beams. But, no accounting for taste.

5/8" might span it, though you'll end up with a lot of 6" scraps due to 90 rather than 96" spacing. 1/2" not a chance - it will sag badly.

If you strap it, you only need 1x3, and you don't (IMHO) want it 24" apart which is already a marginal spacing on ceilings - put it 16" or even 12" apart. Actually, if you can find steel resilient channel (AKA furring channel or hat channel or U-channel), that might work just as well and be a lot straighter than the average wood 1x3 or 2x4 you can get these days. 

Might as well insulate up there if you are burying the beams.