My plugin, Sandman Pro, might be up your alley: https://www.plugin-alliance.com/en/products/unfiltered_audio_sandman_pro.html
There’s a free 14-day demo. It doesn’t do layered looping, but the frozen buffer can be modulated in a variety of ways. It’s as clean and neutral as possible, except for the “Tape Delay” mode which has variable soft saturation and wow/flutter.
To contribute to this thread outside of self promotion, my favorite standalone delay is the Eventide H9. It’s the only standalone effects box that I own other than the Analog Heat, as I feel that those two are different enough from plugins to justify the cost (space and money).
In Euro, Rainmaker is my favorite, although programming it can be a bit tedious. I’ve written a number of performance presets that I typically go back to. The stereo delay modes in Warps Parasite are very, very solid.
In software, outside of our Unfiltered stuff, I use:
bx_delay (https://www.plugin-alliance.com/en/products/bx_delay2500.html): Expensive, but worth picking up on sale. I think that this is probably the cleanest delay I’ve heard, as I modulate the hell out of it with Bitwig and haven’t heard any artifacts. As an example, the multi-layered granular-sounding delay on the opening of Telemetry (https://thefebruarythaw.bandcamp.com/album/telemetry-ep) is done with one instance.
Soundtoys Echoboy: I’m a bit late to the party on this one, but we traded plugins after MixCon this year. I’m really impressed at the wide array of internal filtering options, leading to a variety of timbres.
Sonic Charge Permut8: One of my favorite plugins. There’s nothing else like it, and the alternate firmwares are a joy.
GRM Delays: I’ve been using this less since writing Sandman Pro, as the Multi-tap mode was meant to emulate how I use this. Still, it’s a killer unit for layered echoes.
u-he Colour Copy and MFM2: I just picked up the demo for CC, so I’ll see whether it enters my regular arsenal, but they did a great job on the tonality of this. MFM2 used to be my primary delay plugin, although now I find it to be a bit of overkill hahah.
I really think that Ohm Force’s OhmBoyz Infinity is going to be something special when it’s finished. It’s basically a software version of Rainmaker.