You'll probably get a few different opinions on this topic, but let me offer mine...
Personally, I like the Hasbro Softies line of Fraggle Plushes from the mid 80s. Yes, they do have the gaping mouth thing, but they are also made from quality materials and IMO, truly capture the fun-filled spirit of the Fraggles.
The Hasbro line includes the main Fraggle five, Uncle Traveling Matt, and two doozers. Some of the dolls are a bit difficult to come by and can get kind of expensive, but worth it. At least to me.
You might also consider the TOMY Sprocket from the 80s. Again, kind of hard to come by and expensive when you do, but one like into his loveable eyes and you'll be bidding up a storm.
As far as other versions of Fraggle Dolls. The Tomy plushes are relatively easy to come by, save for Mokey and Sprocket (and Uncle Matt to include his original hat, pack, and boots, which seem to be missing often). TOMY has the distinction of being closet to the real thing in terms of materials used to created the dolls. However, their heads seem quite small in relation to their bodies.
The relatively recent Sabbaba plushes are pretty good as well, but there's not Mokey, Uncle Matt, or Sprocket available.
The Manhattan Toys versions are pretty good overall, but each character has been a bit off in some ways. Not bad for the most part, but just lacking that extra magic that screams Fraggle Rock. That said, if I were to buy a second set myself (I do have the entire Hasbro Softies line + a TOMY Sprocket), which I do plan on doing one day, the Manhattan Toys versions are the ones I'd get.
Hope that helps a bit.