Hello, and welcome!
I have been fortunate thus far to never encounter a sticky or shedding tape. However, I have read some and watched some videos enough to know that some do attempt to bake their tapes with a food dehydrator. This keeps the layers together for a few weeks, I think I got that right, after it's cooled for a day. The tape doesn't disintegrate or anything after that. It just gives you a window of time to play it back with much less or no stick/shed of the tape so you don't harm the tape/player irreparably during playback and you get much better video playback quality.
TGrant Photo is a great place that offers a product customized for this job, if you were to ever consider doing it yourself. I am not sure he does any video capture for people. But he sells a lot of refurbished or custom gear for us that DIY. His site appears to be down at the moment I post this, but it was up recently. So, I cannot find the exact link to the product, but it may be linked from this informative article on the topic I found via search engine.
https://www.tgrantphoto.com/sales/in...ng-video-tapes There are others I've seen on youtube that have done this on their own with a dehydrator for probably less cost. Since I haven't done this, I don't know how much difference there would be between his custom product, and just getting something straight off the shelf. The big thing seems to be the temperature used, and it is rather particular with not much room for changes. So if the gear you have doesn't keep accurate temperature, that's probably why his has a thermometer built in so you can be sure you get the right levels.
No experience with services. Not much I can volunteer. But I suspect you'll get more replies. What has been said a lot is that the quality of services out there can fluctuate quite a bit. So even if they were good at baking it, they may not necessarily use the video gear you'd like to get the best out of your tape. As you'll learn from this site everything in the video chain matters with regards to quality of capture. The player, proc amp, external TBC, capture device. It depends on how particular you might be. So asking for advice on services is wise, as there are probably some that should be avoided.