a1b2c3,

As you can't get H1b from normal quota for this year, there is always non-profit organization H1b called "Cap-Exempt H1b category". In this category, can file h1b any time of the year regardless of the H1b quota. Most of the University jobs non-profit organization (I heard some hospitals as well, not sure about that) are like that and they can file H1b any time of the year and can start working as soon as it approves.
But there are some down sides, if you want to transfer H1b to any private companies, you have to again go through H1b quotas. You can always transfer to another public institutions. I think, this is best choice in this type of situation.

Hope that helps.