Every system has its own set of compromises, benefits, and system-specific issues.
The “no-cleaning” for Piston weapons is a massive myth. If you aren’t running a suppressor, you’re going to get much less carbon in the receiver/BCG/Bolt area; however, you’re trading that off for pure nastiness in the piston area. It’s easier to clean, but it still needs to be cleaned. It doesn’t do away with cleaning of the BCG/Bolt/Receiver, since you will still get funk in it, just not as much. So, at the end of the day, you’re still having to clean.
I’ve had the opportunity to shoot 2 different piston ARs, both owned by two different buddies, so my experience is limited to what I was able to witness with a small sampling. I currently own an unfired Ruger SR-556; unfired because I refuse to shoot it until I either get a PWS Enhanced Receiver extension: http://www.primaryweapons.com/STORE/PC/viewPrd.asp?idproduct=139&idcategory=, and/or Seth Harness’/Firearm Ready Solutions Anti-Carrier-Tilt Buffer: https://www.m4carbine.net/showthread.php?t=15453 .
Which leads me to your specific queries:
(1) how does feel and handling compare to conventional gas AR’s, both in actual shooting but also overall weight, balance, etc.?
Pretty similar. The shooting I did with my buddy’s SR-556 seemed pretty much like a normal AR, but with a slightly lower perceivable recoil impulse. I attribute this in part to weight, and possibly the short-stroke piston. There is a definite increase in weight in the piston-ARs that I’ve shot (SR-556 & POF 415). On my personal one, I’ve kept the flashlight and optic small and lightweight as to not exaggerate the weight (Single-Stage Surefire E2L & Trijicon RMR).

It seems lighter than my M&P15:

Obviously hardware/accessories choices play a part in this.
(2) how does reliability compare?
I don’t think there’s a gap, just different issues. The benefit to the DI systems is damned-near universal parts compatibility. This takes the logistics in regards to parts resupply out of the equation. With the piston systems, even if failure rates were demonstrably lower, which doesn’t seem to be the case, parts breakage is a bigger headache, since you’re typically dealing with proprietary, first-party hardware. Third-party support is essentially nonexistent for piston systems.
(3) what cleaning and other maintenance issues are there?
I don’t know why, but the manufacturers of PS seem to recommend not lubing as much as a DI AR. My personal stance is that they can, in the nicest way possible, go fly a kite. I did a lube-down of my SR-556 like I was going to go saltwater diving with it. Maybe I’m a stubborn mule, but metal on metal, creates friction, which creates heat, which creates problems. I’ll keep it wet.
The biggest issue that seems to present itself with the PS ARs is carrier-tilt. This is when the asymmetrical force of the op-rod is driving the carrier downward and dragging in the receiver extension.

Allegedly, it will eventually stop after a certain point, but this is why I’ve been shooting my DI ARs until I decide on a system to mitigate the tilt. Right now I’m leaning towards Seth’s ACT buffer. The ACT buffer has a nipple on it which is custom-fitted to your BCG. The BCG rests in this nipple, preventing it from tilting as it is thrust back into your tube.
https://www.m4carbine.net/showpost.php?p=357465&postcount=161
https://www.m4carbine.net/showpost.php?p=174294&postcount=1
(4) what makes and models are particularly of note (especially any folders)?
If I were going to buy a piston system right now, my main criterion for purchase would primarily be that the system was designed from the ground-up and not a retrofit. That’s just me. PSs are shoe-horned enough already into direct-impingement design, so, my mystical snake-oil beliefs are that any issues with a PS are going to be compounded by further forcing it into an AR by retro-fitting. That’s an unfounded/unresearched opinion, but I’m barfing it out there anyway.
If I had no AR, and wanted one, a piston-system would not be my first choice. Since you already own a DI weapon, you may want to delve into the piston realm. I’d recommend the SR-556, but frankly, I’ve only shot around 700 rounds out of my buddy’s, and I don’t consider relaxed, range shooting hard-use, nor a suitable test. FWIW, there were no issues encountered whatsoever, but the ammo was cheap, 55-grain Remington green-box ball.
I bought the Ruger because I honestly believed HK would never release the MR556. Though not experienced in my limited handling of the POF 415, I keep hearing errornet rumours about them not being able to make it through a class without some sort of issue. That’s why I went with the SR-556, since I did have a lot of positive experience in shooting with someone else’s. Again, I don’t know of anyone that’s done a class with one, so…
Robb (GotM4) didn’t have anything positive to say about the SR-556, nor did Grant (C4I Grant), and they are two individuals whose opinion I take seriously.
Frankly, 700 rounds isn’t enough for me to make a definitive conclusion on, but the only issue that I saw was wicked carrier-tilt; hence my reservations about shooting mine until I muster the scratch to score a fix. I’ve got myself spread pretty thin financially between my “Man-Cave” project and working on my backyard Zen garden, and the M&P15 is my main go-to smokewagon, so I’m not in a rush to get the Ruger “in the game”.
Just my limited experience, and opinion. Hope it helps.