Nearly all of my trips to DLR are solo (I'll be there next month, too!), although I don't eat table service too often. Napa Rose Lounge is great -- one of my fave spots to stop in to relax and get a drink and a bite. I believe you can order off the full menu, although I generally just order the mac and cheese or a pizzette (while the bartender crafts a yummy cocktail!).
If you want the full Carthay Circle menu, you'll need to book a reservation. The lounge has a separate menu and won't serve the dining room menu. I've eaten in the dining room a couple of times and never had an issue getting a reservation the same day. I just booked on the app for the next available reservation (maybe an hour in advance) when I felt like eating there. If you book for 2 people it's usually easier to find a reservation and the CMs are fine with you switching it to one person when you show up to check-in.
It seems any more that the table service restaurants in DL/DCA require reservations -- it's rare that I hear walk-ups being accepted or enduring anything less than a couple of hours wait. If you aren't picky about what time you eat, you can generally find a reservation time available the day before (or even the day of). It's easier to quickly reserve on the app so then you'll know you'll get a seat and can use the time in between to go on a ride or catch a show instead of just waiting around hoping the buzzer will go off. I think the only place where a last-minute res won't work is Blue Bayou -- that generally books up at least a week or two out, although if you keep checking, there might be a last-minute cancellation that will open up.
I'm not too sure about the DTD restaurants since I don't usually venture out there for meals, but I believe most of them have a bar where you could order the full menu.
