I've never tried tumbling a stabilized rock as it's way too much work to go through for a tumbled rock.
Although the epoxy(s) used to stabilize is/are pretty hard I doubt if it would fair well during the tumbling process but this is just a guess.
desertdweller has a tutorial on her stabilizing process here somewhere but she doesn't tumble but rather cabs her rocks.
In any case,,,it's a very long,fairly complicated process no matter which type epoxy or method you use so again,,,I wouldn't bother doing it for tumbling.
--------------------------------------------------------------------------------------
Your rocks are looking pretty good and to answer your question about a soap/borax burnish,,,,,,,I don't do it per say.
I don't like borax as I find it can leave a white film on my rocks,,,,,,ONLY MY opinion!
When my rocks come out of the barrel I put them into a colander and rinse them off into a bucket using warm water with soap powder.
I then hit them with a hard spray until I don't see any gray water coming out of the bottom of the colander.
I then put the rocks into a container with soap and warm water and slosh them around before hitting them with another hard spray of cold water.
If ,,,and only if some of my rocks have "problem" areas,,I put them in the barrel with hot water and powdered soap for about 1 hour and then rinse them off before the polish stage,,,,if in fact I do run a polish stage.
I doubt very seriously if you can save that problem cab without grinding down past the eroded/pitted area(s).That area is too deep for an epoxy to do much good and would end up looking lousy anyway,,,,in my opinion.
I "think" I can see grit and or slurry in that area and if you let that cab(or any other rock) dry out,,,it will be VERY difficult to get that grit and or slurry out.
You MUST get it out at EVERY wash/rinse while it's still wet and fresh out of the barrel and coated with soap.
Do not wash or rinse rocks like this but rather take them and is you don't have a VERY hard spray to hit them with,,,use a tooth brush and some bar soap to scrub the grit/slurry out.
,,,,,,,,,,,,,,,,,,now this is where some of might differ in our opinion about a soap/borax burnish.
Some people swear by the burnish and can get this grit/slurry out in that burnish but,,,,again,,,in my opinion and in my experience I have found that this burnish only helps to erode the problem areas more.
To back up a bit here,,,,,,
IF you want VERY good quality polished rocks,,,the ONLY time you should see pitted,flawed,cracked areas is during the rough stage.
If you've passed rocks with any type of flaw into the 2nd stage it wasn't ready for it!
The exception to this is when you are deliberately doing rocks that you KNOW have flaws but still want to polish them or when you are doing a specimen piece that you want to leave as natural looking as possible with a "polished face"!
So as not to confuse you (moreLOL),,,this is an example of what I call a specimen piece.
It's a piece of Arizona Petrified wood that is chuck full of fractures and also has some pitted areas.
This is typical of this type material and I knew if I broke it up to tumble there would only be very small pieces of it left so I did it as a "specimen piece",,,,,,
Here is a close-up of a "problem area" that could hold grit/slurry/polish if not taken care of along the way of the entire process,,,,
I may be drifting off here a tad by including the "specimen pieces" but I want to show you that there are many,many different "avenues" to consider.
To me,,,,,,as a beginner I would try my best to do only quality material(s),,,,get that down pat and then move on to other problem rocks.
ALLLLLLLLLLLLLLLL of this comes with trial,error and experience,,,
What I always try to do is to help you to not make the same mistakes I've made,,,,,the rest is all up to each of you as individuals as if we are all artists sitting and drawing a bowl of fruit.EVERY picture will be different but they will all be that same bowl of fruit.
Good Luck,,,
connrock