Well, as to the Brooklyn part, this is a route I ride often:

From President and Prospect Park West:
Down President,
Rt on 3rd Ave
L on Bergen for just 2 blocks
R Bond St
L Pacific St
R Smith
L Schermerhorn and then I continue on towards Brooklyn Heights. I think you could go right on Boerum Place which'll take you up past the Marriott and towards the bridges. As mentioned above, you can get there by Smith.

A nice alternative to the problem with Jay St. is, if you continue on that little road next to the Brooklyn Bridge entrance (I think it's Adams), past the apartment towers, it hooks to your right and meets up with the Manh. Bdge, much less traffic this way. My route is a crazy zig-zag that mostly avoids traffic, although 3rd can be a bit of an adventure.

One of these days I have to try the zacster route.

And I will certainly try Stacy's route too because my western routes from Manh Bdge have been unsatisfactory.