I have to admit, this is the first time I have ever heard of having an average cap AND handiap. Usually it is one of the other. I agree with what has been posted before, if I see something that has an average cap, I am not going to enter into it unless I have a team that is near the cap. If the cap is 840, I want to be at least 830 or 835 (depending on the situation, in a league I would probably go with 830, but in a tournament setting I would want to be closer to 835 and up). If you are giving handicap, let the averages go as high as they want, the handicap should make up for it.
Just one little story about handicap, about 5-6 years ago, I was bowling in the Houston city tournament. I came in as basically a scratch bowler (they based handicap off the highest average in the city, I think it was 90% but I don't remember, so I got something like 4-5 pins a game). I shot over 2300 for those 9 games (had 810 and 786 in D/S). I finished second in scratch, by about 4-5 pins. But both the guy that won ( a very good bowler in his own right) and I finished in the mid teen to early 20's in Handicap. While I had no illusuions or complaints about not finishing second in Handicap too, I found it disheartening that we were both non-competitive in the Handicap side. I think first was well over 2400 (over 800 a set). I find it hard to believe one can average over 255 scratch and not be competitive in Handicap as well. To me, that shows that something is broken. Now maybe I am having a Gizmo moment here, and I will get flamed for this, but I am willing to take it. I don't mind giving handicap, but to me this shows that something is out of whack.