We have always entered the park on the west side of 47 and I think Washington street where the wooden bridge is...never had any issues.
Only thing I would suggest is about 10 blocks before you get to the bridge, make a right off of 47 and head west to the street that the bridge is on. You will avoid all that traffic as you will be west already.
No need to head all the way down to Seneca and waste all that gas. Not sure if the ramps down by the resturant are public or if they are private for the marinas and you would have to pay a launch fee.