Question about 110E stock

Been reading up and depending how my first range session turns out, may be doing a stock and pillar bedding job on the new arrival.

While checking it out and taking it apart, I noticed the barrel is pretty much free floating from the chamber on in the forearm area.

Except one spot about a half inch in near the end of the forearm. This is obviously intended to be there.

If I pillar and glass bed the stock, should this be taken down for a full free float of the forearm or leave it in place? Have only seen one reference to this anywhere on another forum and it said not to touch it but was part of a stock refinishing post, not a pillar and bed post.

Also, since most of the chamber up is free floating now, other than some strengthening of the forearm area, what is gained by putting bedding in the forearm?

Thanks.

Personally I would leave it be to start with. Too many unknowns at this point to say anything else since we don't even have a base-line accuracy to work from as it sits. Too many people just want to jump in and blindly throw money at their guns when they have no clue what they're starting with or what it may or may not need.

Take it out and shoot it for awhile to familiarize yourself with it and it's quirks, then start thinking about solutions for those quirks.

That is the first thought, just leave it as is. Will keep the spouse happier and prevent me from being called the "dearly departed Michigun" for a while, anyway.

I'm not looking for a 500 yard sub-MOA rifle or I would have bought one already set up as such and probably not a 30 year old 30-06 with a $50 Tasco scope.
Just wanted a dependable bolt action that would not break the bank now or in the future.

The preference is to find another used 110 LA blind mag stock in walnut and keep the original as is.
Barring that, I would like to refinish the stock at some point. It is not in bad condition, just looks like wood grain vinyl that you see on cheap stereo speakers.
But if I am going that far, might as well look at doing it all at the same time.