OK, I'll play...
If I am going with a 5.56, I guess it would mean that my stockpile of 7.62x51 is all out and I haven't killed any machine gunners in a while.
But I do believe in having a 5.56 for backup, if only to have something set up all like I like it that uses the police and military's main cartridge. In my lineup that is an AR, just for parts commonality and the ability to customize it to my liking, but I'll play by your rules...
I would want something pretty light weight, but I like a long barrel for increased max effective range and ballistic effectiveness with the little .22 cal projectile. I think 20" is pretty much ideal, but I would sport an 18" if I had to. I would also want a 1/7 twist rate, so I could use the heavier bullets that are effective at longer ranges... my strategy in a "combat" situation would be to stay out of the enemy's max effective range but keep them within mine, if at all possible. I would also want a chrome-lined bore, for increased reliability and ease of cleaning.
About the only thing I see that fits the bill is an FN SCAR 16 LB. It weighs a trim 7.74 lbs., and it has an 18" 1/7 twist chrome lined barrel. Top her off with a TA-11 ACOG, a surefire light, about 15 p-mags, and a GI M-14 sling. They already come with KAC's excellent folding iron sights, which are a must-have.
Hmm, I like it almost as much as my ideal AR setup... except for the fact that if something breaks on that FN, it will be damn near impossible to find parts if things have deteriorated so badly that we are in the middle of a shooting war in the continental U.S.
If you really have somebody who has offered to pay for a rifle set up however you want, then you better stay on good terms with that person. Friends like that are hard to come by!
Oh, and why did you mention the M-1 in your original post? As far as I know, nobody has ever converted one of those fine battle implements into a poodle shooter. And if you know of somebody who has, please let me know so I can liberate it from them and restore it's manhood.