I am a strong proponent of feeding queens, I do it with all of mine, and I have yet to have 1 eat an egg. They are actually laying eggs like crazy!
As far as yours not tending the brood, just make sure the area is warm. She will work through her issues. If she is eating that means she has not given up (my first ant queen did this, because I did everything wrong..), so just make sure she is warm and fed. And try not to bother her too much (no more than once a day checking on her).
Just relax. Ants will do what they feel like doing. If she is fertile, you should be good. I find honey to be very helpful in getting fully-claustral queens to start laying, give that a shot! Very potent, and does not mold easy. Fairly easy to put a drop in a closed test tube without worry about it molding (takes about a month in my experiences to mold in an ant environment). GL! don't stress!
feeding queens can produce different results with every queen. some queens will (who are claustral) will feel uncomfortable with anything but her and her brood in her chamber and may cause her to eat her eggs as she feels the chamber is compromised. this won't happen for every ant but i feel that if you have a claustral queen why risk adding stress and just let her do what she does naturally
The thought here, is that it is very hard to know for sure how well fed the queen was when she flew from the nest. Also, if a queen is starving, that is going to cause more stress. So if she is bumped and gets any more stressed she will eat her eggs in case she needs to run. Even in the wild, queens will deal with some interruptions. And if food is dropped into their nest, they will eat it.
I feed my queens to give them the best chance of success as possible. I am sure some will not like it (I do have a carpenter ant that refuses to eat, I stopped trying to feed her and have her locked away now. I have a strong feeling she is infertile though), so I definitely agree its not a 100% approach. But from my testing, it has been enormously successful in feeding the queens. Especially after hibernation, I couldn't get the honey on the wall fast enough, they were eating it right off the toothpick. Seeing how much their gasters grew, they were starving. Within 2 days of feeding 4 out of the 5 queens started laying their first eggs.
Recently I gave 3 founding queens with larvae a section of meal worm, within a basic test tube setup with no workers. All 3 were eating within 5 minutes, and were running back a forth eating more then feeding their larvae. I won't say at this point it was 100% the right thing to do, more testing is needed, but at this point I have to think that it will make the larva more healthy going forward since they were fed more.
I will continue with my testing with the queens I get this coming year, and let you know how it goes!
A thought: Nature provides humans with the ability to go about a month without food, I doubt anyone likes to go more than half a day without food. Nature provides queens the ability to go the entire founding process without food, I doubt they like waiting that long to eat! I bet they will feel a lot more comfortable if they are full and don't have to worry about starving! They will probably feel a lot better about laying more eggs as well since they have so much food to give.