Great! Without that first shot its not a bad shooting gun!. What did you have done to it?
It says a lot about the Mini-30 when you get excited about a 3 inch 10 shot group with a first shot flier. It wasn't just one thing that I did to get the group size down, but several. I suspect that all were trying to overcome a barrel that is too light to have the operating rod, stock and gas block all hanging on it and bouncing around at each shot.
1. Glass bed the action. 2. Bed the fore arm into the gas block. 3. Addition of an UltiMAK hand guard. 4. Addition of an Accu-Strut LT.
All of the changes made to the rifle made an improvement to the accuracy of the rifle without hurting the reliability. It never has failed to fire or function.
If I had to do just one that I thought would affect the accuracy the first thing I would do would be bed the fore arm tip into the gas block. This was done by glassing shims to the fore arm metal until as tight a fit as possible was obtained that would still allow the dis-assembly of the rifle. It was the least expensive change, took the least amount of time to do and I think made the most difference in my rifle.
The second would be glass the action. That action/stock fit is really loose and has to move around a lot when the rifle is fired. I doubt seriously that it is in the same place in the stock after each stock. With glass bedding it will be closer. This was not easy to do.
Next would be the addition of the UltiMak hand guard and last would be the Accu-Strut.Both of these serve to stiffen the barrel although I'm not sure how much. While they add a good bit of weight, they both made a positive difference in the group size and that tells me that the barrel needs some kind of support. Both are easy to install and mostly just bolt on. If you follow the directions, it won't be a problem.
If you look at a Ruger Mini 14/30 you realize that the slide is not really attached to anything and doesn't ride on any thing like a guide rod. It just goes back and fourth in a huge channel in the stock and can't get out because the barrel is blocking it from the top. The first thought that popped into my mind when I saw this is it will probably never fail to function, but why bother with a rifled barrel?
I never have been able to figure out the first shot flier...Probably has to do with the fact that the first round is chambered by hand and the rest are chambered by the violent operating of the action.
While I'm not a gunsmith and did the work on this rifle my self, I had the close supervision of a good gunsmith keeping me on the straight and narrow. He has built Mini-14's that were true minute of angle rifles. He did it by replacing the barrel with a heavy barrel and making the necessary changes to the gas block so that the barrel didn't have to be reduced in size. He told me that he wouldn't do another one, even for himself.
Both the Ruger Mini-30 and Mini-14 are screaming out for a barrel that is heavier between the action and the gas block and a gas block that is big enough to handle it with out reducing the size of the barrel.
It wasn't just one thing that I did to get the group size down, but several. I suspect that all were trying to overcome a barrel that is too light to have the operating rod, stock and gas block all hanging on it and bouncing around at each shot. 
