There used to be/is a fan box & bar that you install from the 'room' side. The bar has guide feet that sit on the topside of the ceiling rock. You cut the hole, push any insulation out of the way, insert the bar thru the hole. You tighten the support bar thru the 4"round cutout hole; it has barbs that penetrate the joists. Then you mount the box to the bar. Done.
There are similar 'kits' available at the big box stores.
I still like the 'old way' of a 2x4 and a listed box.
As to keeping the box flush to the sheetrock to work from above, using the 8/32 box screws mount a 6-8" flat stick (or metal) & when you pull the box up, the face will be flush w/ the rock.