But...why? I mean, you could do that, but a cheaper/easier/pragmatic solution is just to log the offsets between barrels. My Gen 1 has had up to 12 barrels at any given time and whenever I swap a barrel, I just not the offset to zero difference and add it to my DOPE. That's also a reason I switched to using Field Firing Solutions way back when: because you could store those offsets in each rifle (barrel) profile so that it's a seamless process.
If you've only got a few barrels, just zero your scope to your most commonly used barrel/load. Then shoot your other barrel/loads and note the offset. For example, my 26" 6.5x47L barrel is 0.0 Up and 0.0 Right. The 20" 6.5x47L barrel is 0.1 U and 0.2 R. 16" .308WIN is -1.0U 0.5 L, etc