You can get good results, and you can get bad results. Each bullet and cartridge load is a rule into it's self.
The Sierra, Hornady, and Speer 170gr FN are good "dual purpose" bullets. They are "tough enough" that they won't blow up at close range/high velocities. They will expand considerably which will limit the penetration. I suggest you use a starting load of H4895 or IMR3031, RL15, or IMR4064 in the '06. Limit the velocities of these bullet in the .300winmag to that of .30/06 loads.
The 150's and lighter are a little bit different story. The Remington Corlokts, I suggest you stick with the proper bullets. These are superb in the .30/30 for which they are designed. Especially with the 150's, they will be a bit soft for the .30/06 and far too soft for the .300mag. Such that they may even run pressures up too much. I've seen the 150's expand excessively even from the .30/30 when run to about 2,400fps as can be done with warm hand-loads (BTDT, but the deer died "quickly", to say the least!).
The Speer 130, 150, and 170gr "Hot-Core" flat-nose will be the best candidate for this purpose. I've used them, as well as the 150 and 170gr Sierra's for the stated purpose and had good results.
But, you won't save any money as these days, these bullets cost the same or more than the appropriate bullets. I recommend that you use the Sierra 150gr ProHunter Pt.Spt in the '06 and .300. They are cheaper than the 170gr .30/30 bullets and will work splendidly with even starting loads of the faster burning powders as they are intended to do such in cartidges such as the .300Savage, ect......