You don't wanna use synthetic in a fresh rebuild. Wait till its due for a change. If you're worried about oil, just stick with Kohler brand oil.
Sounds like ya need to download a free service manual from Kohler, pay attention to the lifter bleed/install procedures.
" But let me tell you something ,folks: You can't fix stupid!
There's not a pill you can take, there's not a class you can go to. Stupid is forever!"