Yeah, wild game, being the healthy treat that it is, is low in fat, and its tricky to get things done while maintaining moistness. But its better to have a drier bird than a case of nasty food poisoning. Your using apple pie shots? Are you talking about schnapps? The span sounds interesting. We live only 30 miles from the Hormel plant in Austin Mn. I love span, but have never thought about smoking one. I bet that will taste great. Will have to try that one.
Also, once your temps get to say around 150-155 degrees, maybe wrap that bird up in some foil and let it baste in its own juices. That should really help to keep things moist.
Post some pics of the end results if you can.