One possible solution is to pretty much remove the Sarlacc entirely in either of it's current forms.
When we see it it's either in isolation or framed in by sets.
Once in a while there is a live action element that crosses the field of the Sarlacc in either it's physical set or CGI forms but they could be isolated for later use.
A redesigned physical model could be built and dropped into the space, it needn't be life sized, the Sarlacc isn't as huge as the sand worms in Dune so scaling down the sand isn't as much of an issue as it was for that movie. Though the bigger the model the better the effect (I'm not trying to underplay how difficult this would be, designing a model and building it, matching the lighting and reintegrating the live action elements would be a massive undertaking).
So like much of what is being proposed here it's not so much impossible but difficult.
For me part of the problem is the written ambition of the script doesn't match the resources available on the location and that's something that can only be augmented with CGI in a limited way.
Stuck with the footage as it was originally framed I think the beak and extra tentacles was as much as they could do back in 1997 (they couldn't move the creature so they added parts to it and animated those).
Threepio in the script describes Carkoon as a pit and the nesting place of the Sarlacc but the location is more of a dent in the sand.
Ideally the pit should be more rocky (so sand doesn't fall in it as much) and when the barge first turns up it would be great if the Sarlacc wasn't there and was enticed to the surface by the sound of the party arriving.
It would be visually much more interesting to see a giant Lovecraftian sand/sea monster heaving it's way up a stony pit than just having a sand crater with a sexually worrying mouth already hanging open in it.
Star Wars is always at it's best when it takes the visual language of one cinematic genre and turns it on it's side.
The sequence was meant to evoke images from maritime adventures (pirate ships, sea monsters, walking the plank etc) but it's a little too conservative with it's references so it would help to revisit some of those films and see what works and try and figure out what can be put into the existing footage in a convincing way.
Angel's mockups show the potential of shifting the live action elements around to compose much more interesting shots.
As with so much in ROTJ the problem isn't so much the story but the presentation not doing the story justice.