"...165 grn. might be a little too heavy..." Nope. The rifle was designed to use .30 M1 ammo with a 174.5 grain bullet, not .30 M2's 152 grain bullet.
"...Canadian .30-06 ammo dated from early 50s..." .30 AP used in the 1919 .30 Browning MG. Used until the MG's were converted to 7.62 NATO. It won't hurt your rifle, but it likely has some collector value.