I used to say tisaleim because that was how I heard my father sing it. Then I heard my Rav say tisalum. I looked in a bentcher and saw that it said tisalum. Every siddur/bentcher I’ve checked since says tisalum. So now I say tisalum. I actually showed one of my brothers that, and he was surprised to see it.
I usually say meheirah also.
If you want to see an interesting nussach for Yedid nefesh, look in the Koren siddur. R’ Sacks saw an original manuscript from the author of Yedid Nefesh that had different words. He put those words into the siddur.