I'd stick with the Manhattan Bridge route, which is the route I take on my commute to the Grand Central area. I use Prospect Park and Vanderbilt, and take either Dekalb or Myrtle Ave to Ashland/Navy st, and then Sands St. Once in Manhattan I go right on Canal at the end of the bridge, left onto the bike lane on Allen St, which becomes 1st Avenue. 1st Avenue has a brand new bike lane being put onto it (it may be finished now, I haven't been on it in 2 weeks.) Use 2nd Avenue coming back which takes you straight down to the bridge. Coming back to Brooklyn I always take a left on Myrtle as no other street goes through the entire way to Vanderbilt without getting into some traffic.

If you stay on Ocean Parkway past Church Ave, on the one way WITH the traffic (not on the expressway of course) you'll curve around to the entrance to Prospect Park. You will be on bike lanes almost the entire ride if you follow this, which is pretty amazing considering the distance.

And I agree with the panniers. It is much easier to ride with the bag on the bike than on your back.