Congrats on buying one of the few "new best maker's" double rifles! I was talking with a friend about this concept in the wee hours of the morning today.
First, what causes the variance? If you've established its always the case that one barrel is lower velocity than the other, it indicates that one barrel is tighter due to machining irregularities. What can you do to close the speed difference? You can open the tighter barrel to slow the velocity. That is operating under the assumption that a pressure spike from the tight barrel results in increased velocity. The ways to do that without damaging the rifle in a manner that lapping could do would be as follows.
Meticulously clean the tight barrel with all the good stuff. Shooters choice / Sweets, then wipe out, etc. Rotating through all the brands may dissolve stuck particles in the bore or rifling that is restricting the bullet. After that, you can use a bronze brush rolled in bronze wool, with a cotton patch soaked in JB Bore Paste and Kroil. 50 strokes, then a full cleaning. Do this up to three times. You haven't lapped the barrel, but you certainly have attempted to remove microscopic debris and burrs that may result in lower pressure.
If the former improves it, great. If not, next step would be to use pin gauges and a bore mic to see if there is one area of the bore that happens to be tighter than it should. If that is the case, and you can localize it, then a competent barrel mechanic will lap the bore in that area, staying far clear of the chamber and muzzle of a double rifle. (this is professional's work)
The good news is your gun will be more accurate at the end of the process. The bad news is that your current regulating loads may not be correct any longer, because they probably were converging due to one barrel effectively being crooked...one barrel was yawing more by the velocity difference. If you correct the barrel problem, you may find your new regulating load needs to be a grain more or less than it is when you started.
