C172 transitioning TEB and EWR Class D; voiced concern regarding ATC's failure to initiate proper inter facility handoff's; resulting in potential conflict with helicopter traffic and Class B incursion.

Narrative

On initial contact with TEB Tower; I requested transition southbound and handoff EWR landing LDJ. I was cleared to maintain at or below 1;400 FT. I transition from TEB Tower and when on GSP southbound; Controller advised of helicopter traffic at 900 FT. I responded traffic in sight maintaining visual separation; TEB Controller approved. I was asked to contact EWR Tower. EWR Tower Controller mentioned about the helicopter traffic which I responded traffic in sight maintaining visual separation; which EWR Controller approved. EWR Tower Controller mentioned that TEB Controller didn't arrange the handoff with Approach. He mentioned that he will try to arrange; but to remain clear of the Class B airspace. I was at 1;400 FT MSL and he asked me to maintain 1;000 FT. I maintained visual separation with the helicopter at all times. EWR Controller said that approach was not picking up the phone and that I needed to circumnavigate the Class B airspace. He asked me to squawk VFR and frequency change. I did a very steep turn and remained clear of the Class B and Class D airspaces for TEB and CDW. There is a corridor of 2.0 miles separation between the TEB and CDW airspaces. I contacted CDW and asked for transition; which was granted. The CDW Controller mentioned that TEB called and said that next time I enter their airspace to contact them first. I mentioned that I was with TEB and they didn't get the handoff with EWR; which I had to then turn around and circumnavigate. I feel that there is a hole in the system as the Class B ceiling begins at 1;500 FT MSL. The TEB Controller didn't properly arrange the handoff perhaps because I was clear of Class B. I was concerned for my safety and the safety of the people in the ground. I was trapped in this tiny airspace. I could not climb; descend; and/or turn due to the incoming helicopter. I did slow flight until the helicopter passed and began a 180 degree turn watching my radius and position in the GPS while maintaining visual separation with the helicopter.