Hello:
I actually posted a similar question several weeks ago and got no responses, so I did my own research and then found one on Craigslist that works perfectly.
The best solution is the most expensive. There are inversion table that have bars above the ankles that you can hang gravity boots from. Gravity boots have the advantage that you actually buckle your soon-to-be-victim in them securely, so they can't wriggle out. As I mentioned, the downside is the boots tend to add quite a bit to the inversion table cost. Here's an example.
http://store.devinesuperstore.com/teeter-hang-ups-ep-550.html
I didn't go this route, but I did want to find a table that at least allows you to tighten down the bars around her ankles so that she's snugly in. And also, as you mentioned, it has to have a removable foot bar so that you can get full access to her helpless soles.
In my Craigslist search I ended up choosing a Teeter Hang Ups F5000. It has the adjustable ankle bars (well padded) and you can unscrew a knob and pull the foot bar completely off. Bad news is it's an older model and I dont think Teeter makes it any more. However, you can find similar tables with these same features as well.
http://www.kaboodle.com/reviews/teeter-hang-ups-f5000-inversion-table
My wife's good friend came over recently and had to try it. Fortunately, she was wearing flip-flops and kicked them off right away, and she got in. I had to reach in between her feet to unscrew the knob holding the foot bar in place, which took 10 long seconds. I have decided to replace that knob with a pin that I can easily pull to get that bar off. You will be rewarded with a pair of bare soles directly in your face. I tickled her for really no more than 5-10 seconds, and her feet didn't move an inch but her laughter indicated that she really wished she could!
OK, so the downside of the inversion table is that she's hanging upside down and laughing with blood rushing to her head. So you really wont be able to engage in a nice long session without making her uncomfortable. Really it's just a way to engage in a little bit of tickling on someone you might never have the opportunity to.
Hope this helps!