[clawhammer]

I'm looking to build up a budget gravel/commuter bike with the Sora 9-speed groupset I'm pulling from my latest road bike. It doesn't need to be anything fancy, just something that can handle gravel/dirt roads and still be decent on the pavement. I'm pretty new to anything off-road, and I'm aiming to stay under about $400 for tires, wheels, brakes, and frame or forks.

I'll get a set of canti brakes, 40mm tires, and 36-spoke wheels, but I'm having trouble figuring out what to do for the frame. I've got a relatively new entry-level Trek hybrid (FX 7.0) that seems like it could be a good starting point, but the stem is a cheapo threaded quill stem with integrated handlebars and I need to replace the flat bars with drop bars. Is there any point to trying to find new forks for the Trek, or should I be looking for a used steel frame? Is it feasible to find a decent frame for under $200?