Are you most concerned about corrosion resistance or strength?
Either way I would suggest that you find some 316LN filler wire.
Though if corrosion resistance is key you may want to go over alloyed on the filler.
The welding should be more like 316L to 316L since they are both Mo grades.
I'm not concerned too badly about corrosion resistance nor strength. Basically I'm edge welding the two materials together using GTAW on a weld lathe. It's like a seal weld.
If I understand you correctly, you are saying the heat input for XM-19 is similar to that for 316L. You've given me enough that I can make some samples and try it.