Ah yes, the age-old oh-lord-I-tipped-over-my-dinner problem. Back when I used a Svea 123 — a stove many readers still swear by (or at) — this was a constant issue. The Svea had a contact area that was about two inches across, and if the pot wasn’t perfectly centered over it, the risk of a tip-over was constant.
And it remains a problem with most stoves that employ the upside-down-rocket-ship design approach, which puts the fuel tank or canister directly below the booster nozzle… I mean, stove burner. Which reminds me of another Svea story, which took place many years ago. My 123’s burner had gotten clogged with a piece of sand, which despite repeated cleanings I could not dislodge. Apparently I also believed the problem was due to inadequate pressure, so I kept priming the thing with priming paste. Finally, the pressure inside the stove got high enough to blast out the obstruction. Now, Sveas always were noisy stoves, but the roar this thing made was unbelievable. Like a 747 at takeoff. And flames shot out about 12 inches from each side of the burner. Take off the deflector plate, strap it to a rock, and NORAD radar would have picked that thing up!
Anyway, I digress. You may find the solution to your problem in the Primus Footrest ($8). This is a little spider-like gadget that has three legs that splay out from a center structure designed to clip onto MOST fuel canister. Your Twister is pretty ecumenical when it comes to canisters — just about any will work — so you should be able to find a match between Footrest/stove/canister. And that, simply put, should solve the problem.