My drilling will put three rounds into a neat group, and only after that, if I continue without letting it cool, will I start to see the POI climbing (and even then, not by 3"). My BBF would do the same. I wonder whether the extent to which yours is stringing the shots has something to do with the sleeving? Residual stress in the barrel insert for example, or arising from the sleeving process?

Most times in the field I suppose it would not be a problem, as long as you make the first shot count, but if nothing else it would be good to know that it is consistent, so that if a second shot was necessary right after the first you could allow for it.

On the brass issue, I had a .222 Rimmed, and the Bertram brass was un-headstamped. Rather than use .357 Max to form it, and have cases that are underlength, you could use 5.6x50R brass, such as the excellent RWS which I use in my 5.6 single shot.