I so so feel for you. My daughter has autism, adhd and anxiety. Relatively low on the autism spectrum, I think if you didn't know you might just think she is full of energy and bossy as she masks very well out, and then breakdown at home. We have had similar issues, she desperately wants friends and parties. We spend an absolute fortune, invite 20 people, about 10 actually show. But! Over the years we have build friendships, and now that same 8 girls (plus her and her sister) are at our parties. Church was a good place to make friends, and, similar to you at dance. She just needed help, we would go over and over good ways to start conversations, give her a fidget bracelet to try and reduce her hugging people! Once she has made the friendships, people realise she is very loyal, kind and clever, and understand her bossiness is her need for things to be right. For example, when playing barbies last week, she was worked up because one girl wanted the princess doll to go milk a cow, and my daughter was like a princess wasn't do that! And I don't have a barbie cow! The cow is a squshimellow! You can't mix them! But she's learnt if the game isn't going how she goes, she can say she needs a drink and step away for a minute, and her friends have learnt, through parents, everyone is different and Grace likes things to be right.
Personally I would try for a big party, invite loads, as long as some turn up, yes it might be wasted money, but she will be happy. Pizza straight from dance and pamper evening sounds good. Her home will be her safe space so less pressure. Pizza hut cater for every allergy going and I don't know any teenager who doesn't like it! Or, as she loves dancing, tickets to a concert definitely sound like a winner as people wouldn't just not turn up, just invite say 3 just in case 1 is genieunly ill or awful lol.
This website is helpful. Good luck.