I missed this the first time I read your post, but the pedal jumping forward sounds like a damaged hub. One or more of the pawls and/or engagement points within the hub may be worn or damaged. If so, you're probably looking at replacing the hub. If it's just gunked up you may be able to fix it by cleaning it out with a degreaser and re-lubing it.
This is probably not part of your problem, but an FYI: I'm not sure about the cog, but depending on which
Surly chainring you are using, they recommend a 5-8 speed chain or a 6-9 speed chain rather than the 1/8" ss specific chain. I use a 94mm BCD 32t Surly chainring on my singlespeeds with an 8 speed chain. This combination has always worked well for me. The closer fitting chain causes less drive train wear.