Well... Believe it or not, there are options here. I think if I'm reading the original poster correctly the lack of choice of what to do is what's really disturbing about the situation. So here's an idea or two.
Faerie Queens are ancient, jaw-droppingly intelligent, make Machiavelli look like someone's cute kid brother who thinks he's figured out the world at the age of 5, and oh yeah, they're SCARY because the only thing protecting you from all the worst they have to offer is protocol and your guy apparently giggled and threw that out the window.
You have a couple of different options for this. All of them should probably feel like they have a real "... Without a Paddle" sort of Aspect to them. To start with, they have him cold. It sounds like Aurora will be well and truly hacked off at him. But she doesn't have to swat him down out of hand. In fact, that might be entirely too quick for her sense of justice. What she really wants to do to him might take years to fully play out. Remember, if it's worth the wait... she's got the time. So, in light of that, she can...
1. Subcontract out the hit. What if all the best and brightest of the Summer Court (and those that want to think they are) are offered a chance to rectify the situation for her?
2. Use the PC as her whipping boy. The worst, nastiest jobs with the least possibility to get out of them in one piece... Yeah, he just volunteered and she can hit him with malignant magic at any time if he tries to stray or say no.
3. A curse. This is the sort of situation where faeries traditionally level some real doozies on mortals. He already owes her from taking an oath and breaking it. She doesn't need a path in, he handed her one. Be creative.
4. The character screwed up so badly that she isn't willing to move against him yet. The full shattering awfulness she wants to inflict upon him simply isn't ready yet. He'll likely be in for a most unpleasant time if he attempts to walk through that portal but they'll let him squirm and maybe even talk himself into thinking he's weaseled out of it. But he hasn't. The beauty of this plan is you get to put off vengeance for later. Then at some dramatically appropriate time, well that's when the faerie queen foresaw his time of greatest trouble and acts to end his life in a moment of extreme despair. But on the way out he might have a choice. He might be able to act in a way that lets him get in a full dramatic death scene and make a difference in the world before he dies. An example of this from Changes might be Mab getting torqued at the Red Court for not respecting her turf or her Accords but doing absolutely nothing for a good long while until she sees her chance and sends the Winter Knight and her most powerful sorceress to even the score at the end. If she'd sent aid earlier things would have resolved themselves much more favorably for the Red Court in the end.
This list is mostly ranked from simplest and most direct to more involved and subtle. Generally what's going to save the character (at least in the short term) is the queen underestimating him or putting off immediate vengeance for something much worse later on. Giving time always allows the possibility that the character will trip over a way out of the predicament. If he'd managed to screw Summer any other way I'd say Winter might be a possible ally but realistically they have no more use for oathbreakers than Summer does.