Ponderous, at some point every team in FIRST has "looked like a fool".

You're SUPPOSED to be asking questions, how else will you learn? You can feel comfortable asking questions of your peers here in this forum.
However, be sure that you're familiar with all the rules that appear in the Game Manual - there may be a section that talks about using a velcro-like substance with the ball - I suspect it might damage the surface and usually that is prohibited, but that's just my opinion. [I haven't read the manual yet myself since I'm not on an FRC team and so I cannot point you to the proper section.]
Next, check the Question and Answers (Q&A) forums to see if another team has already asked this question of the game design committee. If you don't see the question, post it there to get the official response. Never trust an answer found here on Chief Delphi as being "official" - always check with the game design committee. The link to the Q&A should be posted soon at:
http://www.usfirst.org/community/frc...nt.aspx?id=456
Good luck this season!