I've done several of these rehab projects and would like to share my thoughts on this. The most important thing to remember is patients and diligence, as this can go sideways and create a bigger mess.
DO NOT..repeat..DO NOT use a heat gun to remove the carpet covering. The goal is to remove as much of the carpet as possible then deal with the residual adhesive later.
TOOLS:
1) Screw driver (to remove existing hardware)
2) Sharp carpet knife
3) Straight edge (yard stick? level? 2x4?, something long and relatively straight)
4) Metal putty knife, or wide chisel
Prep:
1) Remove all exterior hardware and grill. Leave the input panel for now. Place the individual screws in their own jar or sandwich baggie and label them as to where they go. EX. "corners" "grill" "handles" etc.
2) Remove the drivers. Use a piece of masking tape to tape together the two leads of each driver and label them. EX. "top right" "bottom left" etc. Photo documenting this is also a good idea.
3) Leave the ports in the baffle. They are probably glued in and will break if you try to remove them. Personally, I would leave the baffle as-is and not try to strip it. It will provide a good substraight for the drivers, and is probably still in good condition.
4) Remove the input panel-crossover-cables in one piece.
Messy stuff:
PATIENTS...TAKE YOUR TIME...
1) Start with the back. Learn your lessons on a part that won't be as visible
2) With the carpet knife and straight edge, score a checkerboard pattern of approx. 6"x6" blocks. Don't cut too deep, just enough to cut the carpet and not damage too much wood. You are creating an array of manageable carpet blocks to remove.
3) Start with a center block as it probably doesn't have as much adhesive as the edges. Use the carpet knife and putty knife to start prying up the edges of the block. If it starts to pull, stretch, or tear, move to another area of the block. See if you can keep the block intact and remove it completely. The first few will be a learning process, but you'll get better and faster as you get a feel for it.
4) Remove all carpet blocks from the back. Take a break and congratulate yourself for a job well done.
5) Repeat steps 1-4 for all remaining sides except the baffle.
Report back on how that goes then we can talk about getting that nasty residual adhesive off.