There is no such word in English as participantses.
There is variation that you could use for plural possessive
- participants's, janitors's
- which is usually shorted to participants', janitors'.
It is not just a plural possessive issue. It is a possessive issue of whenever the possessing noun ends with "s".
- A genius's intellect
- A genius' intellect
Pronouncing participants's is obviously "participantses".
However, how to pronounce the abridged and normally written version participants', is subject to differences in preferences.
You could pronounce it as
- participants's (i.e. "participantses")
Occasionally, I prefer to pronounce participants' like I would participants's, which is "participantses".
That occasional preference of mine is for clarity, but sounds awkward. Awkward because
- users' sounds horrible as "userses"
- nurses' sounds horrible as "nurseses"
- the shops' hours sounds horrible as "the shopses hours"
- Jeff Bridges' career sounds horrible as "Jeff Bridgeses career"