Erik_A's suggestion is pretty good for keeping within your budget if you can find the right donor bike, preferably something with a frame that you could get something for in resale. Don't worry too much about what wheels are "strong enough" for CX and gravel grinding. Any well built wheel is up to the task. Any poorly built wheel will have problems. Use whatever wheels you can get in budget and check the spoke tension.

Aksium wheels are decent and you can usually find them in near new condition for around $150.

Used STI type shifters are always a gamble. You never know how much life they have left. Often they work great for a long time. Once in a while they are near the end of their useful lifespan. It's impossible tell just from looking at a picture. An alternative is a new set of Retroshift shifters, which are great for CX and gravel grinding and have that magic combination of being cheap, light and strong.

I wouldn't worry about component level for the cassette. You frequently see new bikes spec'd with 105 drivetrains and a Tiagra cassette or Ultegra drivetrain with a 105 cassette. There's a minor weight difference between levels of Shimano cassettes. The biggest difference is finish, which is just about irrelevant after one ride.

The bottom bracket you have is a bit of an albatross. You may be able to find a decent ISIS crankset cheap on eBay (be sure to measure the spindle to verify that you'll get the right chainline), but you may be better off just replacing the bottom bracket to open up your options. Either way, at your budget, I'd go cheap for now and plan to maybe upgrade later if you think you need to. A good crankset would eat most of your budget and if you're going to cheap out you may as well go really cheap.

Don't forget room in your budget for cables. A good set of clean cables makes a bigger difference in shifting and braking performance than an upgrade in component level.