The TP-16 was revised at least two times that I know of. Each version had a different "headshell" design. I think one version actually had a removable headshell with a bayonet-style mount, and another had the removable armwand and a more traditional-looking headshell but it still required an unusual cartridge mounting technique as there were still no slots at the top. Why Thorens designed them this way, I have no idea.
I believe the last few years of the TD160 used the TP90 tonearm, which has what you're looking for. Perhaps the armwand is interchangeable with your TP16. The problem is, Thorens parts are rare and expensive and so this might be out of your comfort level in terms of experimentation.
The easiest solution in my opinion would be to swap out the arm completely for a Rega or Jelco or something in the $300-$400 range. I've also heard that the Linn Basik Plus and Akito work pretty well on Thorens decks. And, of course, if you came across a trashed parts unit with a TP90 arm, I don't see any reason why you couldn't swap arms.
I believe the last few years of the TD160 used the TP90 tonearm, which has what you're looking for. Perhaps the armwand is interchangeable with your TP16. The problem is, Thorens parts are rare and expensive and so this might be out of your comfort level in terms of experimentation.
The easiest solution in my opinion would be to swap out the arm completely for a Rega or Jelco or something in the $300-$400 range. I've also heard that the Linn Basik Plus and Akito work pretty well on Thorens decks. And, of course, if you came across a trashed parts unit with a TP90 arm, I don't see any reason why you couldn't swap arms.