We too started with rebuilding an existing troop, in 2 years we have gone from 10 scouts to 55, with 40 showing up for troop meetings. After much consideration and experimentation we hit on the following which seems to be working. First, so that we could get a decent size turn out at events per patrol we went to the 10-12 member size. (So many of the scouts are active in other things, when we were at the 7-8 level only 2 would show up in some of the patrols). This has worked great!!
Second to build the patrols we picked 4 experienced boys and put them in front of the room, and let them each take turns picking someone to be in the patrol. (These Scouts were not necessarily going to be patrol leader.)The person they picked then picked the next person for that patrol. (This way everyone was with at least one person they liked to be with). Scouts had the option of either accepting or not. It was amazing! The dynamics of the patrols included both new and experienced scouts of all ranks. We also allow the Scouts to change patrols if they want and can find another patrol to take them in.
Some folks had a little problem with the last person picked problem like we all experienced in school when choosing up teams. YET, what happened was the Scouts that were picked last were those that never attended outings, or did nothing but sit around if they did attend outings.
This worked even better that we thought, because some very popular Scouts found that their peers recognized they were not contributing to the troop, and they are now participating more actively.
There seems to be no perfect solution to this, especially in the BOY RUN TROOP concept. Boys today are busier than ever, but even at 11,12,13,14 years of age they know they want to camp with people they can depend on. As leaders we all work hard to make the troops succeed, and what works for one troop may not work for others. Luckily our troop has a high percentage of Adult Leaders.
Hope this helps