Some random thoughts...
It is hard to say what the problem is without actually being there and watching your procedure. Even with that caveat, let me jump in...
I assume that your CA is fairly new. I have had very good success with 2P-10, but others like what they are using. So, I will also assume that what you are using is OK. That brings me to your procedure.
First off, I use accelerator all of the time, and I don't have any problems with it. I would emphasize that you must be very careful not to use too much! I do two or three very, very brief shots, and I have my dust collector on so there isn''t much hitting the blank. I then feel the blank and don't add any more CA until there is no drag on my finger as I touch the spinning blank.
I put a drop of CA on a folded paper towel (I actually use something more akin to the paper hand towels that are used in restrooms), and quickly wipe it from side to side. Don't put too much, and don't lolly gag with the application. A quick spritz with the accelerator, feel the blank, and then when it is dry, on a clean portion of the paper towel, apply the next drop.
I sometimes (if the wood is porous) use a couple of coats of thin, then go to the medium. Oft times, I will just go to the medium. I apply 7 to 9 coats of medium and then go to my finishing procedure, which is sand with 400 with the lathe on slow speed, then with the lathe off, sanding laterally. I then check for an even dull sheen and make sure there are no glaring problems with the finish. Then, on to wet sanding with micro mesh.
That said, there are as many techniques as there are finishers. This is just briefly what works for me.
Good luck!