Or, you could buy an MGI Quick-Change-Barrel upper unit, and just switch barrels instead of uppers.
You can switch barrels in about 30 seconds with the QCB system.
It will work with your lower.
It will work with just about any 22LR conversion kit internals also.
Email me if you have questions.
I work with the MGI factory.
If you want to just use your existing 223 upper, you can do that by getting any of the popular 22LR conversion internal kits that will let you use your 223 barrel with 22LR. Just swap out the internal kit for your bolt/carrier unit, use the kit's magazine, and you can shoot 22LR.
However, you may find that a 1/9 or 1/7 twist barrel takes a little velocity away from your 22LR, and you can get better results by using a 1/12 twist barrel. That is one of the reasons why I use the MGI QCB system, because I can use my 1/7 barrel or 1/9 barrel for 223, and the 1/12 barrel for 22LR. I still need to use my Air Force 22LR conversion unit inside the gun, in place of the bolt/carrier unit.