Welcome!
Your 650 is definitely a size smaller than a YM2000 and wouldn't take the same loader.
I think it is more comparable to YM186. Yanmar's YFL650 was the OEM loader for YM186. This loader came from a US or Canada builder that was likely also the builder for Deere's small loader at the time.
I don't know if you will ever find a YFL650 loader but I think it would be the right match.
Kinda related, your post reminded me of this (yes off topic) ... A few years ago I sold a previous YM186D, to replace it with one that has a loader. A neighbor down the lane came to look at it then said he would rather have the Deere 650 he was also looking at that needed repairs - but he had worked as an auto mechanic and repairs didn't bother him. Ok, whatever. I've been driving by his 'new' 650 ever since ... and the engine is still out of it.
Bulldog loader? I thought those came from the importers of VN-refurb Yanmars and had fittings that are only available through a Chinese-tractor specialty dealer. Check this, I could be wrong.