I used to have a saying that I coined myself. I didn't set well with some folks, but I pretty much still believe it is correct. "If you have to ask, you need a hydro"
Here is my thinking on the validity of that statement. If you are an experienced tractor user, and have used various transmissions over the years including all of the variations of the shuttle from the unsynchronized ones up to the Kubota Glideshift which is an extremely complicated, but easy to use and apparently very reliable transmission, then you would not ask. You would KNOW which transmission you needed. But since you have to ask, that means you do not know. And since you do not know, you may or may not be capable right out of the gate of taking the care that is needed for long clutch life. Clutches are fairly easily ruined by novice operators. Hydro machines are bullet proof from novice operators.
Now I could be full of "beans" or something else, but this is what I think.
I think if you make a lot of directional changes as in loader/grapple work of any kind, anyone novice or no will profit from a hydro machine. If you plow in straight lines and rarely change directions or need to vary speed much you will profit from sort of gear machine of which the shuttle tries to improve on maneuverability and more rapid directional changes, but is still basically a gear machine. A mechanical shuttle where you have to clutch all the time to change direction and change gears would be JUST about the last transmission in the world I would choose.
From what you have said your uses are, you need a hydro in the worse way.
As for the dealers recommendations about moving slow and creeping and control and precision, I can tell she has never operated either tractor, or has the qualities of both VERY confused.
As you can tell I have strong opinions, and you may take them or leave them, but this is what I think. I wish you well on what ever you choose.
James