How deep can I go to rechamber?

[COMachinist]

The 7mm Rem is one the lowest pressure mag cartridges out there. At only 61,000 psi saami spec, setting the barrel back only that much is completely safe, as long as the used barrel has not been compromised Ie. from a fire or extreme over pressure. The Win barrel is either 4340 or 4130 steel and heat treated to 115,000 psi.
CH

 

[38super]

60 thou is nothing. Is the barrel bedded? If so, wipe barrel down with shoe polish and fill with JB weld.

 

[tobnpr]

60 thou is nothing. Is the barrel bedded? If so, wipe barrel down with shoe polish and fill with JB weld.

This.
The Winchester tenon at 1" is the same as Tikka, a bit smaller than the more common 1-1/16", but no reason 60 thou would matter.
What you're doing is essentially the same as a typical setback/re-chamber job. 60 thou is almost exactly what's done with a one-revolution setback.

16 tpi= .625/rev.

 

[38super]

0.0625"