I have bullhorns on my single speed. You can just install regular brake levers on them, but routing brake and shifter cables under the bar tape on bullhorns would be tricky.
But I will say that replacing drops with bullhorns will leave you short on hand positions. You may not notice it now, but especially when riding distances on the road I like having the drops down there to lean down and cruise. I also find technical descents on bullhorns to be a bit awkward too.
I would lean towards a longer stem. Another, cheaper option might be if you've considered moving your saddle back? For longer rides, sitting further back and slightly more upright might be more comfortable.