I have a different upper for my Colt HBAR in .22 LR...so that's out as I understand your question. You want to zero using the same bbl. but with a different bolt/carrier/chamber insert? My guess is that it would be different, maybe radically different.
Removing the bolt/ carrier, then sighting down the bore at 25 yds with the rifle securely clamped in a fixture while adjusting the sights to match what you see through the bbl. will get you close. But actual firing with your intended 5.56mm rounds would be necessary beyond that close in zero. IIRC, the US Army used to zero for 1000 inches (83 feet) to get a fairly good zero for ~300 yds. You could Google that and check the distances...
HTH's Rod