There is no "switching" to TPS per se. Once you use the TPS EAD, you are on TPS and your H1b is technically gone. But if you wait for another employer and they file timely for your H1b you should be able to continue on your H1b, provided that the petition gets approved. The catch is that once you use TPS EAD, your H1b should technically be violated. But that only happens if you actually report this usage. There is no tracking system to check if you have used TPS EAD.

Once your new employer files for your H1b within the 60 days you should be locked in for being able to maintaining your H1b. I would refrain from using TPS unless absolutely necessary, because TPS has a few disadvantages.