Why don't you ask Lee? I'm sure he'll be glad to tell you. The more you talk to your gunsmith the better. You trusted him to do the work. You are obviously pleased with the work. Why not ask him how to break the barrel in?
I agree with Eddie...Lee should be able to explain why and how to properly break it in.
I'll give my thoughts, and anyone can take it or leave it.
First, most of what we are "breaking in" is the throat, where the tooling marks run opposite of the rifling and/or lapping direction. There are misconceptions, IMHO, about why we should do a proper break in on ANY newly chambered barrel and it has little to do with the barrel beyond the throat.
When a barrel is chambered, regardless of the care taken or the quality of workmanship in chambering, there will be small burrs and machining marks...I don't care who did the work, unless they ground it. In that case, it would be much less important, but IMO, still should be done.
Those possibly microscopic burrs and machining marks will collect some amount of copper. That copper will then shield the steel from the heat and the flame when firing the gun. Contrary to what some believe, I believe that the flame is what is doing the vast majority of the work in breaking it in...not friction. So, we fire a shot, copper gets laid down...and lets say it only gets laid down on one land..for giggles. Then we continue to shoot, but one land is shielded from the flame by the copper, which tends to build upon itself, thicker still. Here's where the problem starts. The other three lands are exposed to the heat...but one has a copper plating over it. The three clean lands continue to be burnished in and move forward during fire. You only get one chance at this. 3 lands are buning away and one stays as new. Now, we clean the copper away from the whole barrel. Guess what...one land touches the bullet before the rest. How do we correct this...We can't, short of re-cutting the throat.
Another notion that I think is wrongly but widely accepted is that because we may see copper anywhere or near the muzzle, that the barrel must be "rough" at that location. I don't necessarily agree as copper that was pulled from the jacket at the throat will suspend in the flame until pressures and temps drop low enough, and will then re-deposit themselves anywhere up and down the bore. So copper wash at the muzzle may well be copper that was displaced at the throat...where most jacket upset occurs, in the first place. As pressures drop, so do temps. No wonder why we often see copper at the muzzle, as that where pressures and temps are typically lowest. It's also no wonder that long throated barrels ten to foul more at first than short throated ones. I recently chambered a barrel that was on the "big side" for it's caliber. This was for a short range 30 cal for br...very similar to a 30 BR. This created an even shorter throat than a typical zero freebore throat will be in a typical bore. That barrel never showed a sign of copper...not the first bit! That's just one factor though. But keep in mind, barrel makers typically lap to the same finish without regard for caliber or how long the barrel will be throated. Of course, long throats are typically associated with long bearing surfaces, too.
Bottom line, you get one chance at proper break-in, and heat, not friction, is what does the vast majority of it. Generally, very little copper fouling of a new barrel comes from the greatest part of the barrel...most initiates at the throat, where even the best chambering job was likely done with a reamer that cuts in the opposite direction from bullet travel and lapping. The only reason to not go through a proper break-in is laziness, IMO..and with a good chambering job, the work is typically not much of an effort to insure even break-in of the throat and leade area.
This is just my SWAG at why I feel proper break in is worth the effort. Again, you only get one chance at it. This is only my opinion. Feel free to do what you feel like works for you, but talking to your gunsmith is usually good advice. I think Lee will agree with most or all of my opinion, but that's why I stated that this one is just MINE.

--Mike