I've had a lot of experience with hoes, and never thought I'd recommend a 3pt backhoe - but for what you want it is the perfect tool.
You've go the right type of soil and the right type of projects and the right tractor to use it on.
Getting the right 3pt hoe enables you to keep your tractor - Your JD is way too nice of a machine to just get rid of without giving it a chance.
I used to have a 3pt. mounted backhoe, on a 33 hp tractor and it did everything you want to do just fine. In fact, I've had several. The hoe doesn't have to be a JD; several companies make good ones. Yes, good 3pt hoes are expensive, but they maintain their value exceptionally well. If you use it a couple of years you may well find that you can get most or even all of your investment in the hoe back. Good quality used ones get snapped up quick.
You do want to find one that is heavily built and attaches to the tractor well. The very best ones have some sort of sub-frame to take the stress of the hoe. Yes, that means get a good one; not a cheap one. The good news is that your budget is reasonable. I get you can get a good 3pt hoe that fits that budget.
This all works especially well because you only need to dig to a relatively shallow depth. Hoes go way up in price when you start to want them to dig deeper. For what you want there are some nice 3pt hoes - Bradco is one - built real well but the trade-off is that they don't dig very deep.
The tractor hydrauics don't enter into the picture. Most 3pt backhoes - and especially the type you want - will have their own internal hydraulic pump and fluid reservoir which is driven from the tractor PTO.
A older used commercial TLB (tractor/loader/backhoe) is a reasonable option if you like to do mechanical projects. But know that by the time they get down to your budget they are going to require quite a bit of wrench work to get them up to a reasonable working condition - though if you enjoy wrench work it's an OK way to go.. And when you get it done you can sell off the 3pt backhoe that you used on your JD to get dirt work done while you played mechanic to the old TLB...
I know, because I've gone that route myself, some years ago I sold our 3pt backhoe and bought an older TLB with 6000 hrs on it. It's OK; not what I'd recommend for everyone. Not everyone enjoys doing mechanical work. For me, it's a hobby.
I hear you on not wanting to rent. I'm the same way. I like to work on a project when I want to, and not be constrained by having to go rent something.
Good luck,
rScotty