I want to swap out my deep drop Nitto 123s for a pair of bullhorns. With my current bars, I am using a 58 deg, 80mm Nitto JP stem. To switch to bullhorns, do I also need to change my stem to something with a larger angle? What is an appropriate stem angle to use with bullhorns? I do like the position of my bars now, but would like something with more flexibility with regard to hand position, as well as something that's more suited for climbing out of the saddle.

Helpful advice/instruction is most appreciated.