My 2x6's are running front to back.
The duster is home made. but I fixed 2x2's to it (left to right) , to fit the 2x6 joist spacing.
Pre drilled the fixing holes and preloaded with screws.
Mine is only 8' up, so just stood on my TS, you would need a higher platform, or a pair of ladders etc.
up you go, use your back / shoulder to hold it up, loose fit the screws one end. Swivel round and fit the screws the other side tight, swivel back and tighten up the 1st two.
There are all sorts of "helpers" /props you can make , similar to putting up drywall on your own.
thinking about it ... I couldn't get to the top of my 2x6's, but you could go even easier and put/rest the 2x2's on top of your 2x4's .. so it holds it's own weight, then just fix it so it can't move.