Is there another stamp somewhere on the outside of the frame that looks like it could be a date code?

The reason I ask is that though the 'H' does appear it could be one and it would indicate a 1956 production,, the roll markings on the frame show a Westfield, Mass address for the Savage factory.

Savage didn't move their operations there till mid 1960. That included everything from the Chicopee Falls plant,,all Savage, Stevens and Fox gun production.

Date codes are mostly found on the frame outside surfaces on the bottom.
All models of the 3 makes were date code stamped during the use of the marking.
Even the Savage 99 rifles of the period will have the stamping usually on the front curved surface of the lever boss.

Nice looking example of a 311A!