Any contact by anything will affect the harmonics of a free-floated barrel. I'm sure that there are mounts that you can configure to fit your free-float tube.
I use an inexpensive, Leapers mount similar to the ARMS mount, which provides for mounting a laser or other device (I have a Pro Point 3 mounted on mine) mounted on the side and forward of the carrying handle. If you have a flattop, there might be a similar mount, when used with a riser, that'll work in the application that you desire.
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Shoot to kill; they'll stop when they're dead!