if you can't get the old rubber and glue off you could just replace all the wood at that time which will give you a chance to look over the whole rig.
Not sure what your looking to spend but if the wood is already rotted I would replace a larger area to get it all at once.
I have never done a rubber roof but I recall my roof is only glued at the edges because it seems to have stretched areas from the day I got it so maybe your's isnt glued all the way down either.
Orlando isnt far - I am in Saint CLoud and Work / Office is off of Sand Lake and Orange Blossom Trail
2011 Rockwood Mini Lite 2306 - Matt
2004 Dodge Ram 1500 Qaud Cab 4x4 with 35" tires and 3.92 gears, Dynatech Longtube Headers & Fabtech 6" lift + Superchips with shift Tuning
Nights Camped 2011 (37) - 2012 (16)-2013 (2) -2014 (5) -2015(0)
USMC 91 - 95 - F/A-18 Aviation Ordnance