I was a coordinator for my kids' schools for several years. How many boxtops are on the sheets you are using? Some have only10. Some have as many as 25. Would the number of "spaces" you have on each sheet fit onto a sheet reduced in size by half, so that you have 2 'sheets' out of one piece of paper?
I never cared much for the paper sheets anyway. It was a hassle to package them for shipping. What I preferred was using ziplock snack sized bags. They each hold 50 nicely. :)
Maybe if you bought a few boxes of those and wrote on each one "my boxtops" or something and sent them home with the kids? I don't have a real good solution for you.. because I'm sure that you will reduce your participation if you don't send SOMETHING out to them. I had parents send them in in regular envelopes sometimes. Would that work?
ETA: To get the "word out" without using printing/paper sheets, what works best, imo, is to put out signs along the pickup/drop-off route. Like yard sale signs or sandwich board signs. Once a week or something stick a big sign, or a string of signs out that says "Remember to turn in your Boxtop$ this Friday" or something. Put it out on Thursday. You could even enlist parent volunteers to stand by the door with a sign and wave (like all the tax preparers wearing Statue of Liberty costumes do in March and April).