Hmm. Doing a Yahoo search turned up this page at Hyper Dictionary with Thesaurus entries for give-and-take. Not quite halfway down is drumhead justice. Clicking on drumhead gives a page with various definitions related to drinking alcohol:
bender, bloat, blotter, booze, boozehound, boozer, brannigan, bust, drunk, guzzler, inebriate, jag, lush, soak, sot, souse, spree, tear, tippler
Of course, there are no corresponding dictionary or thesaurus entries for the phrase.
Further checking on yDc’s home page under English Dictionaries, specifically the Century Unabriged (1899) Online Dictionary, under drumhead yielded an entry for Drumhead Court Martial with a note to see court martial under court. Proceeding on to court and thence to court martial yielded only the definition of a court martial. But I vaguely remember something about someone sitting on a drum . . .
The next step was the Webster’s 1828, alas, to no avail. Next, the Webster’s 1913. Zilcho. Ditto for the 1911 Encyclopedia Britannica. But, finally, a close match in the Ultralingua English Language Dictionary:
3. drumhead court-martial n. A military court convened to hear urgent charges of offences committed in action.
Further efforts were all to no avail, even the Online Etymology Dictionary. Who has access to an Oxford ED?
From the research so far, I have a feeling it was originally a field court-martial for offences such as desertion, cowardice, mutiny, or dereliction of duty, perhaps with the presiding officer sitting on a drum(head). In some instances it seems to be used as a synomym for a kangaroo court.