Do not put anything in written until it is final. Talk about it first. When every part agrees, write it down.
It is not a bad idea to contact HM directly to talk about offer. But it seems like you wrote a very demanding letter to the HM. You should know that HM is actually on your side under the circumstandance. he is the one who wants you to work. recruiter is just a middle man to give you as little as possible. So sometimes, after banging your head against the wall(recruiter) again and again, talk to the HM and reach out for the higher level to get some of your terms. But do not be mean to HM. You can be mean to your recruiter, but not the HM. If he lost interests in you, you are finished.
You asked for too much in your counter offer. Pick your battle. What is the most important for you, vacation, salary, relo, signing bonus, option? Not everything!
It seems, although your HM was offended by your letter(that is why they withdrew their offer), he probably does not have many choices. So you may still have a chance. But if I were you, I would re-consider the situation. Afterall, you did offend your future manager. In industry, "treat your manager as God" is the Law.
