I think it has something to do with Franz Stephan and the timing of his death. Maria Anna was obviously out of the running. The next one was Mimi, who was strongly resisting her father's plan re: the Duke of Chablais. FS was strongly for it and to be honest, I don't know how Maria Theresa could've overruled him on this - considering he was the head of the family, not her. Most likely, the plan was to get Mimi settled first before Maria Elisabeth. Maria Josepha's match was already decided with Ferdinand of Naples by 1765. FS was strongly against the match with France so that leaves Maria Elisabeth (who was also said to be a "back-up" candidate for Benedetto of Savoy), Maria Amalia, Maria Carolina and Maria Antonia with no firm matches. His death "cleared" the way for Mimi to marry her Albert and MT to formally discuss Marie Antoinette's match with the future Louis XVI (negotiations started only in 1766). That leaves Maria Elisabeth, Maria Amalia and Maria Carolina (before MJ died). Benedetto was still keen on a match and I don't understand the reason that there was no money for Maria Elisabeth to marry her cousin. MT could've split Mimi's extremely generous dowry of 4,000,000 florins (after all she got the Duchy of Teschen). It could also be a way of honoring the last wishes of FS. She could've given a post to Maria Elisabeth and Benedetto too (Archduke Maximilian was to be Governor of Hungary before the post in Cologne was won for him so the centralisation policy was not strongly enforced - it appeared rather selective). Ferdinand of Parma's purported match with Beatrice d'Este was clearly just wishful thinking and an unfounded dream of the minister Du Tillot: her grandfather and father were both very much pro-Austria and Francesco III of Modena served as Governor of Milan; also, Beatrice was first engaged to Leopold at age one, the year Ferdinand of Parma was born (1751). I don't know about the Orleans princess for Parma but Charles III of Spain seemed keen on cementing Spain's relationship with Austria and he seemed to have carried more weight on this matter as Parma was a branch of Bourbon-Spain, not Bourbon-France. The other Bourbon marriages were finalized after FS died.
I can see why Maria Elisabeth, married or not, was bitter about not having an establishment of her own: MT spent a fortune on palaces for other members of the family and gave them significant posts. But there seemed nothing at all for her. Even Maria Anna's home in Klagenfurt was a palace (known now as the Episcopal Palace) built by MT for her (1769-1776). ME, of course, did not need a palace for there was already one in Innsbruck (assuming she was to stay there eventually; I think MT wanted them to stay in Vienna after her death). However, it did seem that MT didn't give her much thought or showed her special attention through such things.
Oh, an earlier post on their allowances: younger sons got 40,000 florins not 20,000 so Maria Anna got double (later reduced when she went to Klagenfurt). I've read that ME's allowance in Innsbruck was 50,000 florins.