While already established as not eligible equipment, I think you would be MUCH handicapping yourself, big bullet or not, shooting ML or Slug guns. Not that there aren't slug guns & custom muskets out there that can hit eggs at 150 yards, but that is reaching... A GOOD shooting small caliber varmint rifle, with decent BC bullets would blow them away!
What type of winds are there usually at the egg shoot? To move you 4"+ there would need to be sustained 20mph winds at full value (that constantly blowing your hat off, not just gusts). I just don't see that being the norm but idk... I'm sure it more than likely has to do with the fact that an egg at 150 yards its pretty dang sporting for a mostly unsupported shooting position
If from a bench with rear support, the better rifle would always win (and ya'll would need to run the eggs out MUCH farther). From sticks with no rear support, the better shooter with a little luck on their side is much more important than a rifle that will give you a .042" better margin of error, that's less than .03 MOA @ 150 (.30 cal v/s .22 cal --- do the math, it's not a straight .084" although that's not much advantage either).
A Remington varmint/sendero platform with a beefy scope is all over 12.5-13 pounds. I know several guys that call with similar rifle. I see why that's the upper limit & should be allowed... If you can use that to your advantage, sounds smart to me.