Congrats on the new machine! Hopefully it will do everything you want, I'm sure it will.
I can relate to some of this
I have a basic lawn tractor, which is meeting my needs, but I'm doing more with it now, vs when I bought it. Now I have a dethatcher, aerator, and lawn roller, and I use it to move my 4x7' utility dump trailer around, and to use that trailer as a dump trailer in the yard. My yard is suburban, and not big, but it has some inclines, and I get a little concerned about pulling too hard with a lawn tractor (I replaced the geared transaxle once).
A garden tractor would easily & robustly handle what I'm doing, and would be a nice upgrade, even though it's not really needed yet. So I can understand wanting to use a machine that will readily handle what I need, plus having extra capability, if I want to do something else in the future.
I do like having my own equipment, and not needing to ask to borrow stuff from friends/neighbors. But from what I've read, it's tough to set up a GT with a proper FEL. The recent thread about buckets/scoops was interesting to me, in terms of how limited they are, vs a FEL. I don't know if there are ways to sort of work around this a bit.
If you could just get the mulch *into* the dump cart, would that help with spreading it? I realize it's kind of clunky, or a stretch, but I've seen that Harbor Freight sells a little towable backhoe:
Not as nice as a FEL, of course. But perhaps that sort of product is one option for helping to load the dump trailer? It sounds like a real FEL setup would require a pretty-significant machine, which might also be tougher to maneuver (in addition to adding significantly to the cost, beyond just upgrading to an X7xx, etc). People have mentioned other scoop setups, I think someone mentioned having a winch on their scoop, to help lift the load.