"The picture that was hanging here last year has been in the museum now."
Should I use the present perfect or the present simple with "in the museum"?
How would you change this sentence using a participal "The picture......"?
Well I'm not a teacher but I would rather change this sentence into:
"The picture that has been hanging here last year is in the museum now."
I'm not sure if it's right however, it would make more sense to me as you're saying in perfect that picture in question was "doing" something some time ago and changed said "doing" during time.
If I confused you much further, I'm sorry as I'm not quite good at explaining things :)
The present perfect is not impossible, though we would normally expect some present-time context, such as a blank space on the wall, or a recent-past marker such as 'until very recently'.