By all means, file a formal appeal to the District Advancement Chairman, continue it up the chain (Council, Region, National) if necessary.
However, as previously stated, it this troop is this so far out of line with advancement policies, who knows what else they may be inventing on their own. You may want to switch troops. Get a copy of the completion sheet, I'm sure you will find a troop that will be glad to do things right and accept the merit badges as having been earned.