I have pushed over a lot of trees with my P7010 and never damaged anything but there is always one that requires digging out to get it to move. All you can do is push up against a tree slowly to see if it is rooted rightly for pushing over, if not go to the next one. If you have sandy soil, so much the better for pushing over small trees. At my farm, the pine roots seem to dominate on the north side of the tree so they push over more easily from the south side (not so many roots holding the south side)
I think I would push over as many as I could without damaging my tractor then use a back hoe or excavator to dig out the rest. I worked overseas for many years on an 8/3 week rotation and got lots of work done when home, so I see what you are after.
As for stump grinder, they seem very slow to work and large ones are pretty costly. I think an excavator would be a good purchase for you also, especially if you plan to continue this work as a business since most folks want the stumps removed when reclaiming land. A fairly large excavator should uproot a stump much faster than a stump grinder can remove it especially when you start working the root bundle also.
As for damaging your tractor, I don't know about Kubota or Deere, but my LS has never had any damage to the FEL and I have mistreated it severely moving concrete slabs, rocks and trees. Just go slow, enjoy your 28 days off and what you don't get finished this trip will wait till next month.