Want comparable power to the .300 H&H?
Look at going .30-06 Ackley Improved... Delivers about 100fps gain in velocity over the standard 06 IF (big if), if you are shooting Heavy bullets.
Look at the Sierra manual and compare. Performance about the same as the H&H. Close enough to call it a day. 5 rds in your magazine rather than 3, maybe 6 if you do a Wyatt's mag extension.
If you are set on converting to a magnum boltface ctg .533", I have a spare magnum bolt that is complete which I can swap for your complete .473 bolt. This is a CRF bolt all factory original.
Think I would look at the short-magnums like the SAUM and WSM. Barrels are pretty readily available for CRF hartford guns. Swap bolt with me and buy a .300 WSM barrel off gunbroker or Ebay and you'd be set.
The .300 WSM will be in the same league as the H&H. If want something more Nostalgic and Exotic there's always the .308 Norma aka .30/338.