I think Vito's response pretty much nails it: It boils down to how much you want to spend. I'm certainly no expert, but I've baled (or at least run tractors) with many of the options discussed: At our Northern farm we bale with a selection of old-school, conventional dry-clutch, independent-PTO tractors (usually a White 2-105 or Ford 6600). But one time in a pinch I had the baler on our newer Kubota with a hydraulic shuttle shift. Ours is too small to comfortably run the baler, but the hydraulic shuttle sure is nice. I've also baled for a chap up the road with one of his larger Kubota's with the hydraulic shuttle. I've driven a couple tractors with a mechanical shuttle (though not round baled with one). And at our Southern farm I still bale a few dozen rounds a year with an Allis 180 with the hydraulic power director.
For what little my thoughts might count for, here they are:
The Kubota hydraulic shuttle is superb. The ones I'm familiar with are the late 80's and early 90's L & M series - a conventional gear and clutch trans, but also a hydraulic shuttle you can bump back and forth between fwd, neutral, and reverse without touching the clutch. I think most Kubota's of that era have a valve unknown to many folks (usually behind the lower dash that you have to remove a panel to access) that can be flipped between a 'summer' and 'winter' setting. In the 'winter' setting, it's a little more aggressive with the hydraulic flow to the shuttle to engage motion a little quicker and more aggressively. We keep ours on the 'summer' setting all the time. Works fine for us in all temperatures, and is a little less aggressive when flipping back and forth between fwd and reverse. In the dead of winter when the fluid's really cold it might take a couple seconds to get up to speed, but nothing that's ever been a problem. One of those hydraulic shuttles would be my preference for round baling if I had to back up a lot. No need to ever hit the clutch once you start baling. I'm sure lots of manufacturers have similar hydraulic shuttles.
Although I've never baled with a mechanical shuttle, I've driven them enough, and I don't really see how a mechanical shuttle would offer much more advantage than a conventional gear trans/dry-clutch for round baling. But others might feel differently.
You original post mentioned the Allis with the PD option. Although that's what I bale with at our Southern farm, it would definitely be at the bottom of my list. The PD isn't going to help you at all for backing up: You'll still have to shift into reverse with the clutch. And if you're thinking of the three-digit or D-series Allis's (which is what most people think of when talking about PD Allis's), they don't have independent PTO, so you're still stopping the baler rolling every time you hit the clutch. And as you probably know, those Allis's were notorious for developing gear jumping issues if you ground the trans into gear a lot. Going back and forth between fwd and reverse several dozen times each hour while round baling will likely result in some gear grinding, regardless of how careful you are. The PD can be handy to avoid using the clutch when round baling, but only if you have a way of baling without backing up - which is what I do (more on that below). But also keep in mind that on any of the three-digit Allis's 60 HP or larger (180/185, 190, 190XT, 220, etc.) they have a hydraulic PD, which is hard to 'feather' like the mechanical ones of the smaller Allis's. They like to engage with quite a jump, unless you have just the right touch. And the hydraulic ones often have a little bit of viscous drag that will want to keep the tractor moving even when the PD is in neutral unless you ride the brakes a little. I've got used to baling with our 180, But again: it would be my bottom choice over a conventional trans with independent PTO or hydraulic shuttle.
One thing you might consider is baling in such a way that avoids backing up. If you're on flat land you could find (or build) a kicker. But even without a kicker, I still don't back up for most of my baling. For the first couple of rounds I don't have any choice because there's no room to turn. But once I'm done the first couple rounds, I never back up. When the tying cycle begins I quickly pull out of the windrow (without stopping) while it's tying and loop around and drive to a spot where I want to dump. As long as you're out of the windrow, you're not going to cause any problems driving while it's tying. Once I'm where I want to dump the bale, I hit the clutch, open the gate to dump the bale, then let out the clutch to keep driving away and into the windrow while I'm closing the gate. Once you get good at timing it and knowing how tight to make your loops, you can usually time it so it's done tying right when you've reached a spot you want to dump, and time it so you're just finished closing the gate and engaging the PTO as you pull back into the windrow: It doesn't take any more time than it would to reverse and sit there idling while it ties, and it saves having to shift. All you need to do is hit the clutch for a couple seconds while you open the gate. I started this practice at our Northern farm where our fields are so hilly that you rarely finish rolling a bale at a spot where you can dump it without it rolling away, so you usually have to find a good spot to place each bale no matter what. But I now do it even on flat land: It saves crashing gears and having to reverse, and usually allows me to place the bales a little closer together in groups so it's faster to pick them up and load on a wagon when bringing them home.