I have not tried the technique of pulling the second valve slide and generally I do not create a huge amount of saliva (I have never had any in my 3rd valve slide). However, in many cases of persistent sticking which occurs only when playing, I have pulled one of the pistons and observed a noticeable amount of saliva on the surface of the piston. It seems that the saliva competes with the oil for whatever clearance exists between the piston and casing and causes drag to occur. One way I have established a correlation is to thorougly wipe the piston and casing and re-oil (very lightly - one drop only) and resume playing. It takes awhile for the sticking to occur again and when it does, I observe the same issue of saliva collecting on the piston.
So, in such cases, I have almost always resolved it by going beyond the normal cleaning (soap, alcohol, vinegar, etc) which is guaranteed not to remove any metal to the following steps in order of agressiveness (each one is done after usual cleaning/drying step):
(1) Wet the piston and then apply a dab of toothpaste (my tech recommends Pepsodent which is still available in the 99cent stores) and smear it around and then insert the piston and work it up and down for awhile. Then again rinse and dry the piston and casing.
(2) Apply a bit of polishing compound with a clean, dry cloth and rub vigorously (this is just a bit more abrasive than the toothpaste).
(3) Try rubbing compound as above (a bit more abrasive still).
(4) Spray the pistons and inside casings with Break Free or REMS Oil (both have teflon) and let them sit for awhile. Then wipe the pistons and casings to remove residue before playing.
After each step, check to see if the problem is solved by appling a light (one drop) of synthetic oil and play it for the typical amount of time it takes for the sticking to show up. If it does, go on to the next step.
Note that the above steps only work in the situation where the clearances are too tight causing the saliva to compete with the oil. The progressive steps will increase the clearances in miniscule amounts making sure it does not go too far. If these do not remove enough, then perhaps lapping by a qualified tech is the next step.
I have had only one case so far where lapping was done - and it was done by Kanstul on an Olds so he certainly knows the issues there. It fixed the problem for good and did not compromise the compression. So, it can work if done correctly in the proper situation.
Good luck with your efforts.