You are, yes, but 90% of my issues go away not using rim brakes in dirty conditions.
For $600 - you decide. As mentioned above the rim/tire setup will likely be different. Most carbon clinchers are wider. That also means wider tires are required. Big mistake - esp on gravel, to have rims wider than tires. For gravel you may want wider tires anyway, but you'd have to and they are heavier. With a narrower alloy rim you could put some thinner 23s on there as well if you ever wanted to race with them (as I think you mentioned you might).
Look at the Shimano Ultegra. My kid got those (team stuff) as his primary off road/trail setup. You can put a 28mm on those too.

I'd put a few hundred $ of value on a name brand too. Certainly Shimano over some less known brand.