[Raul]

How about giving out tokens of 3 different colors which represent different priorities. Use this to determine who gets to play in practice match slots. Here is an example:
Green Token = 1st priority
Yellow Token = 2nd priority
Red Token = 3rd priority
If a regional normally would have 3 practice matches for each team, then give out 3 green, 1 yellow and 1 red tokens. How do we use the tokens? Like this:
As teams line up for a practice match they must hand in a token to get in line. They have to decide how important it is for them to run in that match by using the appropriate priority token. If a team is originally assigned to that match, their green token takes priority over fill-in team’s green token. However, if they ran out of green tokens, then a fill-in team with a green token would have priority over them, since that would indicate that they already had their allotment of 3 matches. This would give teams who could not run early, a better chance of getting in some practice matches later. Fair – right?

To add to this, perhaps you could also say that a red and yellow token cannot be used without first getting an “Inspected” sticker. This forces fill-in teams who have not been inspected to use a green token early. Fair?