I can’t say what that box is worth but I can give you a short history lesson that I won’t charge you anything for.
300 H&H Match cartridges have been around for more years than you or I have, made by both Big Green and Big W. For most of the first half of the 20th Century the 30-06 dominated conventional long range shooting in the United States, however, in 1935, something astounding happened. In that year a shooter named Ben Comfort won the Wimbledon Cup with a rifle chambered for the 300 H&H Magnum, shooting factory match ammo of all things. Popularity of the cartridge picked up immediately but ground to a halt with WW II. After the War shooters returned to the big magnum but when the AMU was created in 1956 the H&H was replaced with the improved versions and that was pretty much the end of it as far as a match cartridge was concerned.
The only boxes of 300 H&H Match ammunition that I have seen are the Remington, like yours, and one by Western hand loaded with 200 grain BT bullets. I have heard that Norma also made match quality H&H cartridges but can’t say when.
Because of it’s short run of popularity I would guess that a box of 300 H&H Match ammo would not be common.
Can you or Ron date that box? I have a 1962 Shooter’s Bible that still shows them being made by both R and W.