Wonder if put it over a tin roof how high or how low above it should one go to make it act as a ground plane.
An old radio buddy put his Imax above his Dental Design Service Shop which was the last suite on the South of the strip center building about >100' feet long North and South, and 40' feet deep East to West. This may be larger than you noted above HM, but it is the only example I'm sure about. He had terrible results with his Imax to the South based on his mount being close to the end of the building and very close to the metal roof.
He set the antenna up in the center of the building about 5' feet from the South end above his shop. The antenna worked fine to the North, East, and West, but it failed miserably to the South.
The building was a flat built-up roof design with corrugated metal supporting the tar and gravel roofing material. He mounted the antenna on a heavy 2' foot high cast iron restroom vent pipe. The antenna was dead toward the south where most of the traffic was located around him in Houston at the time. He said he could hardly hear 5 miles to his buddies to the South.
He ended up moving the antenna North to the next suite about 40' feet away and it worked a little better, but was still noticeably off, so he went to a 20' mast...and then it seemed to work fine in all directions.
IMO, the Imax does not need a ground plane...so you should be OK if you get well above the tin roof.
I'll try and do an Eznec model of this latter, and post it for you to check out. Maybe it will or maybe it won't help us to see the effects I talk about above...where the very large ground plane, in such an example, tends to dominate the RF...and thus ill-effects the pattern's RF higher up than desirable.
I've done something similar to this before and the guy came back and said I was wrong...so you may find different results.