The reason I asked is that I have three kids and a high volume cheap to shoot rifle that is still fun for me is probably in order. A properly chambered .223AI sounds like it could fit the bill. A little more punch but could press the easy button and just buy factory ammo. A bit easier on powder and barrels too.
I enjoy working up loads in rifles and reloading so that's part of the appeal of different calibers.
I like to get many different perspectives as there are often things I haven't thought about.
I honestly don't think there is an option out there that can touch the 223 for your use. The AI sounds right up your alley, the only added cost being another set of dies, but gives you a lot more fun, and options to tinker with (as well as making your brass more durable!)
The real key for you will be building a longer (.060" works great for me!) freebore and using a standard short action with bdl or even better an AICS mag setup.
I have four dependents (all happen to be grown *** men though!) that I load a thousand rounds each a summer for. I do the brass sizing as a separate step, then load giant piles of sub quarter (upper .1xx" to lower .2xx" groups are standard) on my Dillon progressive (RL550 is what I have, but I bet any progress would do the same)
The 223AI is wonderfully efficient and economical… CFE223 has been available almost continuously, and starline sells 1,000 packs of brass with availability about every month or two. For varmints I've used 53g varmageddon, 55g nosler balistic tip seconds, and 53g vmax. All work wonderfully, with lots of great explosive performance out to 500 yards. For target loads I've used 77g Hornady, 70 RDF, and 80g ELD. I'd not recommend the RDF due to finicky tuning, but any target projectile you like will probably work fine.
I've tried 9, 8 and 7 twist barrels, and settled on 8 twist as the best compromise. Still does well with the lighter 53's, and stabilizes up to 80's at least.
HbN coating the projectiles in large batches upped my barrel life from 3k to 4k rounds, which also helps a TON on the economy.
My 80g ELD load is fun for me or anyone, 3100fps MV means it doesn't hit transonic until about 1400 yards!