Stuck mouthpieces
There are a few reasons why a mouthpiece can be "stuck". Not that many really. It could be anything from a drop straight onto the mouthpiece to a longstanding buildup of organic crud and or corrosion.
I've never found one yet that could not be popped off in seconds with nothing more than a small torch for heating (if necessary and it usually isn't) and a plastic or rawhide mallet. Place the receiver against a solid piece of hardwood on a convenient spot on the bench and rap it carefully and repeatedly on its side. If possible, turn the receiver slightly as you work. The vibration and concussion are often enough to get the mouthpiece to come loose. While it sounds simple enough, I have to say that I didn't think of it myself. The procedure was described by a technician. It's worth a try. If they are willing to do it in a shop where they probably have a puller handy then it's certainly worth trying for someone who does not have access to an $80 dollar puller or is far from a shop. I don't think the rawhide mallet would be necessary, perhaps a regular hammer or any weighted object would do if there was no metal-to-metal contact. Perhaps a small block of hardwood or machined plastic or nylon (to act as a buffer) would do the trick.
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A simple mouthpiece puller doesn't have to cost a fortune. Yes, the "brand" ones and the ones sold through official repair tool shops are somewhat expensive, but no-brand ones sold through for instance Amazon, eBay or the chinese webshops/apps are basically the same thing and work just fine, but cost half or even a third of the cost of the "official" ones.
I got one from eBay for about 15€ and it was money well spent.
I got one from eBay for about 15€ and it was money well spent.