Will it squeeze in without any opening up? If not how much relief is needed?

You'll most likely need to open it up a little. I did with my factory KS stock.

Any recommendations on who to send it to to open it up and repaint?

If it is a KS stock for a Remington 700 KS the factory KS barrel contour was between the Mountain Rifle contour and the Sporter contour. Would not take much at all to open it to fit. I would try the barreled action first just in case it may have been a McMillan KS aftermarket stock for a standard barrel.

It has the remington branded recoil pad on it so appears it's a factory ks stock

Yourself.

A piece of dowel rod and sandpaper will do the trick.

Mask it off and shoot it back w a rattle can.

Great.. Are you able to tell which of the three makers built your stock? Brown, McMillan?

OP,
Do you have the stock in hand? What is the known history of the stock?
It does sound as if it is a take off based on the recoil pad. Recall that there is also a magnum ks channel as well, which would not require any opening.
Pics would be very helpful.

Didnt pay enough attention to the corners to tell it it's a brown or mcmillan. Did not know of the magnum ks barrel. I'll have to drop a barrel in it next week and see what it reveals. Regardless, it's got some scuffs and needs a paint job.

I can't comment on McMillan but Brown quoted me $125 plus shipping to refinish a stock.

Just got a sporter barrel set in it and it has a generous free float as it it were a magnum sporter

Yes, that sure looks like a takeoff from a mag ks.

That is as stated above. I took one off my early 375 H&H KS and fit a wood ADL to it and traded it away. I had a M700 270 ADL rebored to 338-06 by Cliff LaBounty in 1994. I taped the barrel to allow free float and bedded the barreled action filling the gaps due to the magnum contour. A bit of rattle can and all was good. The rifle wears a 2.5-8X Vari-X III and weighs a hair over seven pounds. A fair bit of game has been taken with it.