How do you keep from sliding around sitting on top of the plywood and digging with a 36"? Just curious. Heck when I catch a big root or rock on the 24 it just drags my big cat to the hole. Specs on your machine say it weights 7280lbs. Is that sound right?
Were you swinging those boxes off the FEL or the hoe? If the hoe I'm surprised it could lift one let alone swing it in the hole. They do take up a lot of space and at least around here you have to make sure you have enough weight on your GVW. Sounds like you do the set up as well. I've never got into that for the very reasons you stated plus I do other stuff besides grave digging.
But back to your issue at hand. Maybe you already do this but is there any chance of running a set of forks on the FEL and using them to handle the plywood? If the plywood was properly stacked you could use the forks to unload and place them and to pick them up and restack them on your trailer.
Sometimes people are going to complain. They seize upon some detail and have the need to regain some control in the situation. I have a pretty good working relationship with the caretakers but I know what you mean. Sometimes the next level up has "ideas" even though most have never came out and watched the process.
I think turf's will definitely decrease your visible track. Is there anything else you do with the 110 where turf's would cause problems? It would be an expensive experiment to see if its worthwhile but at 7280lbs it just may be the ticket. One of my friends has turf's on a CUT JD and he says it leave almost no track on lawn but won't do anything at all in the mud.
I don't typically sit my machine on plywood for digging, only have plywood under my dirt pile to the side of the grave. However, there are times where the ground is so soft that I do have to put down 4x8 sheets to sit on while I'm digging. Most of the time though I only put a 2' x 4' piece under each out rigger. My riggers have street pads on them, so they do slide back and forth some, but I usually take it nice and slow. Going slow I can feel when it catches on a root or when my machine is about to start sliding, then I can readjust before it happens.
The biggest problem I have with making tracks or ruts is when moving the excess dirt. With a vault I have to make 5 loads (roughly 1/2 cubic yard each), so that's 10 times on the same tracks, plus another 2 times to backfill the hole and get out. Those 5 trips while loaded with all that weight can cause some damage, especially if you're driving over other graves. I had one today where the only way in and out was over 6 other graves and then meander about 150' back and forth between monuments and graves out to the road. I had to spread roughly a 1/2 yard to fill ruts in those 6 graves. That was with plywood pieces down. The plywood just sank into the ground.
As for the weight, 7,280 lbs sounds about right. I axled my whole truck and trailer on the scales one day and the trailer axles with the tractor loaded weighed in at 10,480 lbs. I really should have ran the hoe across by itself to get an accurate weight on it, but I didn't think about it at the time.
When I was setting concrete boxes, I was swinging them with the FEL. I have a utility bed on my truck that is rigged out for all of my setup equipment to keep everything in the dry. I was having to put those c-boxes in the bed, which is about 2 feet too short because of the front compartment that runs the full width of the truck. I would have to lift the box in the air, get off the tractor, back the truck under the swinging box, get back on the tractor, and set the box down into the bed, and then do the same thing at the cemetery to off load. I would use the backhoe for pulling the lids and putting them back on, but only the FEL for lifting them.
As for handling the plywood, what I do now is lay it across my FEL boom. I keep about 8 full 4' x 8' sheets, 6 2'x8' pieces, 4 2'x6' pieces, and 4 2'x4' pieces stacked neatly on my trailer. I always use 3 full sheets under my dirt pile and 2 small pieces under my outriggers, and then any more that I think I may need for driving on and/or to lean against monuments to keep the dirt off of them. I have seriously considered forks, but I've often thought that they may be more trouble than they are worth because I would have to remove them for moving dirt or backfilling, and then put them back on to load the plywood and haul it away.
I estimate (based on my recollection of pricing from the Internet) that it will cost $1,500 to $1,700 to put turf tires all the way around. That is definitely an expensive experiment. Technically, my hoe is only for grave digging, but I occasionally use it around the house and farm, and have done some odd jobs with it for other people such as setting septic tanks, digging trenches for field lines, setting culverts, etc. I think I could make due with turfs.
, and enables me to get back on the road to go dig the next one. 
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