I like to install the pillars first to get the action located where I want it. I normally shim or or use the pillars to hold the action in place for bedding. I do any adjusting before the bedding is applied. The pillars hold the action just off the stock to allow bedding compound to cover all of the bedding surfaces.
After the pillars are set (Bedded in) I use headless action screws to locate/align the action and use spring clamps to seat the action on the pillars to produce stress free bedding. The pillars just hold and level the action and the headless action screws prevent any torque from being applied to the action. I also support the barrel with tape to have a three point contact with the two pillars and the stock. the tape also centers the barrel in the barrel channel and floats it. I use heat shrink tubes to center the headless screws so they don't act as recoil lugs after bedding. (They should not be touching on the sides of the action screws after bedding) After bedding has been allowed to cure, I remove the heat shrink from the headless action screws and replace with the socket head screws that will become action screws. (I like the socket head screws for torquing over the slotted head screws)
The spring clamps only add enough force to push the excess compound out of the bedding area and cannot flex the action.
If done right, I can see no difference in accuracy if bedding the pillars separate or at the same time except for making it easier to get the fit you want before adding bedding compound by installing the pillars first.
There are many different ways to pillar bed an action, I recommend a step by step procedure that allows a potential mistake to be corrected before adding the bedding compound to the stock and action. (If you have ever added the compound only to find out that something is not right, you know what a mess you have on your hands getting it cleaned to start all over).
Just the way I prefer to pillar bed.
J E CUSTOM