Thanks for the input everyone. Here's what I decided to do.
First, I tried taping a thumbtack to my sewing machine deck and doing a circular satin stitch. The problem is, this doesn't work very well for small circles, plus craft felt tends to be a little loose, so structured stitches just ate it up. So that didn't work. Watching how the felt reacted, though, gave me more hope for another technique.
Using my open-toe embroidery/mending foot (if you want to know more about that, ask—it's awesome), I "sketched" out circles staggered down the length of the precut tentacle, using a matching thread. Because of the tensions, what happened is the inner part of the circle bubbled out a little—perfect!
Because these are tentacles and not quilting or apparel, nothing needed to be exact. I just wanted a suggestion of texture/shapes rather than something very overt, so this method worked great. Here are some photos:
This is a close up of the circles with a little bit of stuffing, after being attached to the "upper" part of the tentacle, which is marine vinyl.
This is a finished tentacle, with wire running through it for articulation—part of it anyway; they are about 3 feet long each.
Thanks again for your suggestions! When the whole thing is finished, I'll post it in the appropriate location.