I was in the Marines, where I could "request mast" to jump the chain of command on issues that couldn't be resolved. What is the Army method?

It's called the IG (Inspector General) or the Commander's open door policy. I would encourage you to exhaust all channels before jumping the chain as it's a great way to get noticed.

In the Army we have the Open Door Policy. Here is an example of one. Every unit should have one posted. I would review it and then use that to address any issues you have. If you decide to use the Open Door Policy you will have to notify your leadership that you will be. They can't stop you. If they do then you should go straight to the IG. But first I would try to use the Open Door Policy first. Too many soldiers go straight to the IG. All they will do is check if your unit is in policy. If you didn't use the Open Door then they may just ignore your situation due to there still being means to resolve the issue at your unit's level.

http://www.tradoc.army.mil/SGS/CMDPolicyletters/Policy%20Letter%202,%20Commander's%20Open%20Door.pdf

Was there ever a conclusion to this problem, in the same situation