Are there parsing methods for unorthodox grammatical structures?

The specific parse tree produced for an input depends more on the specific grammar, than on the parsing method, which I take to mean the grammar type (formalism), ie CFG, HPSG, dependency grammar, CCG or the like. If you just mean a specific parser, like the Charniak or Stanford, then I do not know, I would expect most to treat "read" as the head/root. Otherwise you can construct a grammar in any formalism to produce a tree like that, Although I expect most established grammars use "read" as the head, I think categorial or Montagovian grammars might be more likely to work the way you want, since they treat words as higher order functions, and it makes some sense to treat "until" as a function that takes an action and a condition as arguments, but I do not know if that represents current categorial or Montagovian thinking. You could try seeing what the OpenCCG/OpenNLP parser actually does or ask your question on their mailing lists.