Kalle, the International American Football Officials Association Manual of Football Officiating by Jim Briggs has two sections specifically devoted to the responsibilities of the Head Linesman, Line Judge, and Back Judge in 6C Mechanics (6-man mechanics with a centre judge).
Football Officiating Manual said:
7. The following are the valid crew formations we recognise:
Formation Crew size/label Core group Wing group Deep group
120 3 R H, L
220 4 R, U H, L
221 5 R, U H, L B
222 6D R, U H, L F, S
321 6C R, U, C H, L B
223 7 R, U H, L B, F, S
323 8 R, U, C H, L B, F, S
Bossman, a BJ is useful for more than just deep pass plays up the middle. I know, because I have been a BJ and a 6-man deep wing, as well as a line of scrimmage official. I had a play when I was the FJ, and a receiver dove to catch a pass with his back to me. I had no angle whatsoever to rule correctly on that play, and neither did the SJ. The only person who could have had an angle to see that would have been the BJ, but there was none on the field that day (it was only a 6-man HS game in MD), as HL would have been too far, LJ would have not had a good angle, and U's attention would be elsewhere. Other similar plays that are problematic for a 6-man crew, but can be covered well in a 7-man crew include contact by defenders on the inside of receivers on passing plays (At TBFOC, the clinicians showed videos of plays at the college level that were along the sideline where the receiver was grabbed/contacted from the inside, and where only the BJ had a flag, because only he had a good angle. I would assume that similar situations would happen in high school games as well). This is similar to basketball, where a 2-man crew cannot rule properly on plays where there is contact on a ball handler or a shooter opposite the Trail and above the free-throw line extended (That play is in Trail's primary, but he has no good angle to see it. Lead may have an angle, but he should not be looking there, because he has responsibilities elsewhere.), but a 3-man crew can rule properly on that play, because they have an extra official with an inside-out look, just like a football 7-man crew has a Back Judge with an inside-out look to complement the Field Judge and Side Judge's outside-in looks.
I would have to disagree with you on 5 or 6. Personally, I would prefer to work 5-man, because it is easier to build up to 7-man from there by adding two deep wing officials than it would be to move a deep wing with no Back Judge experience to the middle. I know, because I attended the Tom Beard Football Officials Clinic for multiple years as a back judge, even though I started out in a group that did 6-man for their varsity games. It required some adjustments to my perspective to change my keys and areas of responsibility, but with some camp and (semi-pro) game experience, I can be as competent as a 7-man BJ as I was as a 6-man FJ/SJ. In my new association, some of the playoff deep officials (FJ/SJ) are regular season back judges, but others are line of scrimmage officials who move deep, because they can run, and the only adjustments that they have to make are a different starting position and different responsibilities on kick plays (the keys are similar, because both 5-man wings and 7-man deep wings are responsible for the widest man on the line of scrimmage. BJ will pick up the inside receiver on the strong side (same as in 5-man), and the wings in 7-man pick up the backs or other interior receivers on their side who were not picked up by the BJ).