Tino_So who's going to do all of the backend work required to spin up a new thing?
I think it's much better for this new service to be a for-profit endeavor whether it's FACEIT, TF2Center, Stadium, or ABC new service. Nothing can run for free like this, so you have to find a way to monetize.
Ask PugChamp if they're interested in pursuing a new monetization strategy. It's going to sound like a meme but here's what I'd do. I'd put ads on the website just like TFTV. Then I'd modify the PugChamp global chat so that if you subscribe at $4.99 per month you get no ads, a badge in the chat and next to your name on the picking interface, some sick emotes, and something cool in mumble tool (I'd find a way to recolor names or something).
The rest of it would come out of pocket and you can continue to accept donations.
Ask FACEIT to do it. They already have a monetization strategy and a will to develop a TF2 matchmaking system. Problem is, nothing they do for TF2 is because they love TF2. Everything they do for TF2 is really just a test run for a future copy pasta to their CS:GO offering, so if it doesn't work for CS:GO it doesn't work for TF2. I don't think queuing up for a service by class and class-specific skill ratings are something they're interested in developing.
Ask ESEA to do it. They've modified their pug experience in the past and I'd ask them to see if they're still interested in attracting TF2 users to their pug service. The downside with this option is that I guarantee they'd make users pay for ESEA Premium and I don't think it would scale as well if people had to pay to play. Also they have the same problem as FACEIT since everything they develop is for CS:GO and slightly adapted for use in TF2.
Ask TF2Center to do it. The main problem here is that the PugChamp value proposition is significantly different than their current product offering so I'm not sure they'd go for it. TF2Center is all about getting games started quickly with no balancing and you can play with your friends. PugChamp is about creating high quality games with solo queue only.
Ask Valve to do it. This one is also kind of a meme but a bunch of us know the devs and we can at least pitch them the idea of how they can improve their matchmaking service. Of course, they'd pursue their own ruleset, cater mostly to pubbers, and take two years to release a product so this is the worst option in the short term.
Rip the code from the PugChamp GitHub repo and spin up something new, with Erynn and Tsc's permission of course. I asked my coworker to see how much effort it would take to spin up a new service as a pet project and he said maybe 3-4 weeks for a good full stack developer, so I'd just need to see who is available in the community to pursue such an endeavor. Maybe I'd hit up the Stadium guys and see if they're still interested in building things.