I hope this is not off topic.
I install pillars mated directly to the receiver metal to metal.The action is made to free float on purpose from the stock with no bedding compound.The only other contact is the recoil lug and every thing else is relieved of any contact. I used to bed the rear tang but found it did not help any.I only have pillar bedded less than great stocks to help them without machining a bedding block as that would be choice one.
Lets hear it for Johnson's paste wax!

Taking your time you should be able to do a great job of in-letting a perfect metal to wood fit and no pillars or glass is needed.
You can practice using a black iron nipple 4-6" long and a piece of pine wood.The wood is soft and will help you develop a light touch with your scraper and the use of in-letting black.I will tell you once about in-letting black it gets everywhere.Best luck with your project.