I don't think it would work, and here's why. The main problem is the difference in the case head diameter. The '06 is .473", whereas the .458 is .532" The OAL of both cartridges still measure in at 3.340" each, which means theoretically the length of the cartridge would allow it to work in the 7400 action. However, the amount of back thrust from the .532" case head awould be too much for the 7400 action. Plus, you would have to mill out the bolt face on the 7400 bolt. Unfortunately, the bolt face walls are all ready thin at .473, so milling to .532 would not be possible. You would need a larger bolt, which would subsequently require larger receiver and larger barrel extension for the lugs on the bolt (which would also have to be bigger).
So, I guess the answer to your question is no. Unless, of course, you want to build a single receiver, bolt, and barrel from the ground up to accomodate the .458 Magnum in a 7400 style action.
Now, you could possibly rechamber a Browning BAR rifle, as they are factory chambered for the 7mm, .300 Win Mag and .338 Remington magnums. Each of these rounds share the same case head diameter as the .458, so converting one would be possible. I would think any competent smith could do it, but I would not guess it to be cheap. You would need a custom barrel blank milled for the BAR, and regulated for the gas system.
The only question is, why would you want a semi auto .458?