Short to mid range to me is out to 250ish yards.
If mid range for you is 250 yards, I would suggest you probably need a faster twist barrel and a heavier bullet on whatever .223 caliber rifle you have but didn't specify. The National Match/Camp Perry competitions are where shooting at long range lives as far as the numbers of shooters competing is concerned. I would make a small wager that the vast majority of the competitors there are using either commercial or reloaded ammunition with 77 grain bullets. And another small wager that few if any of the competitors there are using ammunition loaded with 62 grain bullets.
NATO nations use 63 grain bullets in their service weapons, and depending on which nation, shoot their qualification matches with those rounds out to about 400 meters (US Marines to 600 meters?), but the ammunition is not that accurate to begin with, nor are the rifles. BUT those rifles do have a faster twist than 1/9" in most if not all cases.
The short story is that the 62/63 grain bullet selection is not optimal for precision accuracy over longer distances. The .223 accuracy at longer ranges crowd are choosing bullets like the Sierra 77 gr Match Kings and similar weight bullets from Hornady, Nosler, etc. Big difference in weight. And barrel twist to stabilize it.
I just helped set up a new barrel manufacturer in Montana. The most popular caliber order we got from manufacturers was .223/5.56, in either 17" or 19" (extra inch to mount for profiling and chambering), and in 1/9" twist.
These were for AR15 manufacturers. We confirmed the twist every single time because they will not stabilize the 70 - 77 grain bullets so popular with AR-15 owners that shoot at ranges beyond what you call mid range (or try to replicate the military OTM round manufactured by Black Hills). They said they knew that and they didn't care because the people buying their rifles didn't care. They were still selling those barrel blanks by the thousands when I left there in October. Why potential buyers of those AR15s (or commercial .223 caliber rifles) would not opt for a barrel with a twist long enough to also stabilize longer, heavier bullets if it were offered is a mystery to me.
On the other hand, when the same manufacturers put in an order for barrel blanks for their rifles in .300 Blackout, they ALWAYS specified a fast twist. Because apparently THOSE customers want a rifle with a barrel that will stabilize a long, long heavy bullet for caliber at lower velocity, maybe because they're all going to put a can on the barrel (unlikely) and/or try to keep their rounds subsonic. So that's what they got.
Related somewhat to what you're apparently doing, I am rebarreling my Ruger 22-250 with a new barrel at 1/7" twist, as well as taking the spacer out of the back of the magazine box so rounds of 75 grains and higher can be loaded to much longer OAL and still fit and feed from the magazine. That's specifically because I want to use those longer, heavier bullets. When I bought the rifle back in the late 70's, 55 grain bullets for reloading was pretty much as heavy as it got, and the barrel twist was just fine for bullets of 45 - 55 grains. Lots of things have changed since then...
If you can get a load with those 62 grain bullets that works well for you at 300+ yards, and you don't shoot where there's much wind to deal with, then you have a winner.