ORIGINAL: tsoc
I also have an 11.5 inch doinker (a blessing and a curse).It has been up and down(that doesn't sound very good)100's of trees.I have never had a problem with it getting in the way.It would seem if your alley way up in to a tree is that narrow you are going to have more problems than just being concerned about your stabilizer.
Mine probably hasnt been up and down as many trees as yours has but it still gets the job done [8D]