the transverses arent that bad. take the lane. The timing of the lights means a lot of cars go by but then you get a couple of minutes with no cars usually. I live on 83rd street i go 2 different ways.
1. across to 5th avenue, down to 72street where you can cut all the way across the park and exit at tavern on the green.
2 across to madison, up to 91st enter the park at engineers gate 90th and 5th and ride through the park to the 103rd st transverse
3. ride right through the park. yes I know bikes aren't supposed to go on paths but I go super slow and if anyone remotely complains I simply say "sir/maam, if i were to get off my bike and walk it, I would take up double the amount of room on the path so I choose to slowly coast through the park" This time of year, the park isn't that busy during the day so it's not that bad. Final option is to enter park at engineers gate and take the bridal path across to 86th and cpw. this is my favorite way. The bridal path is super wide and always filled with young fitness people running not annoying complaining old ladies. provided you have decently wide tires, it's easy to ride on the hard packed dirt. my commuter bike has 32c's with tread so it's great.