Personally, I wouldn't use these rifleman rings, as I must have confidence in something I buy, and for that I prefer steel over aluminum, and steel rings with matching Leupold steel bases that screw into the receiver.
You're talking about the stout recoil of a 308 and a 30-06, and NOT a .22 or a .223. My time and ammo at the range is worth something to me, and I like to know when I install my rings and scopes properly, everything is firmly locked into place. But, I'm pretty orthodox about these things because I demand accuracy and uniform groups, and so always use lapping bars on my rings for the best grip on my scope (and to avoid scratching my expensive scope too), and, I prefer Leupold Dual Dove rings on both the front and back. This way, if I have problems keeping tight groups, I know it ain't the rings!. LOL. But, I'd still glady accept the standard Leupold steel standard dovetail front ring and steel windage back ring set over the budget "Rifeleman" rings. There's nothing more time consuming and annoying to me then having to jack around taking scopes and rings on and off a rifle because I can't be sure if they're doing the job properly. What do they say?...."Spend a little more now and cry less later".