One more old guy vote for a M1 Carbine.
Granted the M-1A would have been my first choice at a 7.62 NATO rifle.....but you already have an AR10. Plus you have a M-1 Rifle which gives you much the same but with an eight round magazine that needs clips and in a caliber that in its military loading is much the same in capabilities.
You do not say what sort of AR15 you built. I am assuming from your other interests that it is HBAR-ish, but for all we know it might be a retro pencil barrel 1-12 twist 16 inch, and a four to seven position CAR or M4 stock carbine. With or without lights, lasers, people sniffer, Passive IR, tilted irons, and bells and whistles though I think with that stuff sort of defeats half the reason for having a carbine.
If this last is your AR, you may be carbinized enough already.
Other wise, what folks have said in the way of good things about a carbine.
Now a lot of the lower case survivalist crowd and nearly all of the Upper Case Survivalist bark about ammo standardization, that is every rifle in the armory using the same ammo. That might be great for Armies with the backing of governments, but diversity allows more ability to use whatever ammo comes along. You already have a poodle shooter and a couple of 600meter plus rifles, an M-1 Carbine allows you to find one more ammo type you can then use.
With shell shrinkers your Garand and AR10 can become single shots if all you can find is .30 carbine. Or you can use a single shot of .30 carbine when hunting for a little less noise if the idea of using a .30 carbine for hunting does not turn you off and still have "full bore" ammo at hand.
The Carbine is light (5.5 pounds) powerful enough for self defense, especially with HP or SP ammo and can reach out a lot further than some folks seem to think if all you want to do is convince someone to go away. There is at least one You Tube video out their of a guy ringing a torso sized steel plate out at 300 yards. Remember when the Carbine was in USA service the average trooper was expected to be able to achieve 50 percent hits on a kneeling man target at 275 yards. Those 110 grain .30 bullets are still doing 1030 to 1040 fps at 300 yards and producing around 260 Foot Pounds of energy.....more than most of the two inch .38 Special revolvers with go fast 110 grain bullets that a lot of anti carbine folks carry for defense at the muzzle, but the carbine does that at 300 yards!
Naturally a good .308 does "better", but even the most carbonized .308 is going to be bigger and bulkier. Certainy if I wanted to hunt big game a .308 is better. For just a bumming around gun or if I was interested in something certainly with the big game range of a more than a common pistol, bow, or BP flint lock ( and a lot of folks seem to hunt large stuff with those 3) I would not feel under armed with the carbine.
In my younger days I was hot for 30 round magazines, but soon learned that 15 is just fine and gets in the way less. At one point I had one of the short "legal hunting mags" for the states that had hunting magazine restrictions, I think it held five shots. I gave it to a buddy because every time I used it I would keep thinking I had dropped my 15 round magazine.
SO just to make it clear.....in your situation I would add a M-1 Carbine next.
-kBob