To be honest, either keep the 223 or get a 22-250.
Ammo is far easier to get, and a lot more choices.
Don't get me wrong, I love my 225s.
I have 2 Win 24" model 70s, a 22" Win model 670, a 24" Handi done on an old 22 jet barrel, a custom 26" Bullberry TC heavy barrel and my pride is an old Remington model 30S Express with a custom 28" Pacnor #5 heavy sporter barrel.
The custom Rem will keep 5 factory under a dime about any time, the 2 model 70s will do almost as good, I have never used the 670, the TC barrel will keep 4 under a dime but always throws 1 out to about a quarter and the Handi doesn't like factory at all.
Brass is getting harder to find since Win dropped production and have heard that factory ammo ain't far behind.
I load a Sierra 52 gr BTHP over BLC2 powder for the Rem and it will cut 1 ragged hole at 150 with 5 shots on a very calm day, both for the wind and me!
Not hard to top 250 factory speeds and the 223 ain't even close but those two are hard rounds to beat in the field.
The 250 and the 225 both have better range and are flatter shooting but I have also made my share of 400 yd + shots on groundhogs with the 223 out of an old 21" TC Contender.
The 225 is a great round and the rim is just an added bonus.
LONGTOM