Since you're 5'3", the number one issue will probably be size and fit. There are definitely carbon road bikes with disc brakes out there in your price range (or a little more), but they may not be available in your size. Finding the bikes in stock to test ride may also be a challenge. What size was your Trek 5200 (top tube length, seat tube length, standover height, etc.)? Don't go by the manufacturer's frame size since that varies widely.

Here's a list of carbon road bikes with disc brakes that might fit you:
- Specialized Ruby Disc (smallest size 44 has 509 mm eff. top tube)
- Cannondale Synapse Carbon SRAM Rival Disc (smallest size 46 has 508 mm eff. top tube)
- Volagi Liscio 2 (smallest size 47 has 505 mm eff. top tube)

Here's a list of carbon road bikes with disc brakes that are probably too big:
- Trek Domane 4.0 Disc (smallest size 50 has 519 mm eff. top tube)
- Giant/Liv Avail Advanced (smallest size 43 has 515 mm eff. top tube)

If you've been riding a carbon bike, a steel bike will definitely not be as responsive. I have a Colnago carbon bike, and two Bianchi steel bikes. They're all a lot of fun to ride, but the carbon bike is much zippier and climbs much more effectively, especially on hilly rides. There are also lighter steel "race" bikes vs heavier steel touring bikes. My Bianchi Eros Donna and Vigorelli are on the lighter, racier side, and they're a lot of fun to ride on longer rides (100 km+) with just a seatbag. The steel Bianchi Vigorelli 105 is available in a 46 (510 mm top tube), but it doesn't have disc brakes.

Keep in mind that lighter steel bikes are not as stable with a load (e.g. 5 lbs. of folders, books, etc. on a rear rack). I definitely wouldn't be comfortable riding my steel bikes carrying 10+ lbs. of groceries or heavier loads for touring. The Surly Disk Trucker and Straggler both have disc brakes, but these are much heavier bikes and will feel really sluggish compared to lighter steel bikes and especially compared to carbon bikes. I had a 2008 Bianchi Volpe that I hated riding since it felt like a tank compared to my lighter steel bike, and the Tiagra components did not shift as smoothly as the 105 groupset on my other bike. The Volpe is now available in a size 46 with disc brakes, but it has Tiagra components.

What kind of multi-day rides are you considering? If you want to do loaded touring, then the Surly Disc Trucker or Straggler may be a good choice. In your price range, you may even be able to get a custom steel frame with Shimano Ultegra components and better wheels. If your multi-day rides are more credit-card touring with just a seat bag, then you may want to consider getting two bikes, a carbon disc bike for your longer rides and a used hybrid (e.g. Jamis Coda, Kona Dew, etc.) or high-end 1990s cromoly mountain bike (e.g. Trek 990/970/950, Giant ATX 780/770/760, etc.) for your short in-town errands and grocery runs. You can usually find barely used small hybrid bikes and steel mountain bikes for about $150-300 on craigslist.