The Alberts have similar tuning issues, however they become much better if the register vent is drilled out to 3/64"

The wooden one I got from Moresky on Aliexpress was cheap but not very well made as the tone holes were very poorly finished. The one from eBay was a bit better than the hard rubber version but still had intonation problems that needed to be addressed.

Unfortunately it is not a Buffet. The trill key guide is not consistent with a 19th century Buffet and the locking screws are of a type that Buffet never used at any point in history.

Generally "bass clarinet" pads made by Pisoni, Music Medic and other manufacturers are made thinner (usually around 3.2-3.5mm) than sax pads (3.8+mm). Most bass clarinets including Vitos need a mix of the thinner bass clarinet pads on the top and sax pads on the bottom. For example, On a Buffet I just overhauled I used Ferree's B32s (3.2mm) for everything from RH2 up and B42s (4.7mm) For RH3 downward. This is pretty standard on most bass clarinets. I would not try to use sax pads on the top end of the instrument.

If a Rico 2.5 feels stuffy that's a big problem...

First I would try a new mouthpiece since you should always upgrade that anyway and you can use them with any clarinet. I like the Fobes Debut. If that doesn't help look for a refurbished Vito or Yamaha, you can get them for $150-$250. It's not worth having your Jean Paul repaired as the pads they use tend to fail quickly anyway.

They made white basses and altos. I had the upper joint form a bass once but sold it. They seem to pop up occasionally and sell for surprisingly low prices.

Not all altos, this is just a good example of what happens when a company gives up...

I'm sure if Selmer put the same attention into their clarinets that they do to their saxophones it would be a much better instrument.

Yamaha 26s are always 3/64” or under though. The only way the cork would need to be thicker is if someone shaved the plastic down, in which case OP should probably have the tenon replaced as now that would be a weak spot. But that’s a very unlikely situation.

If you have problems getting the right thickness I would highly recommend a good set of calipers. You can wrap the cork around the tenon and compress it a bit with the calipers to get a good estimate of what the compressed diameter will be. Using this method I’ve never had to replace a cork because I used the wrong size.