On the subject of radar handovers, sometimes when the receiving controller is busy he/she will instruct the controller attempting the handover to "freecall it". Some controllers prefer it like that rather than receive the handover over the phone whilst planes are constantly chirping away in his/her other ear. I certainly agree a freecall can be just as speedy providing your dealing with switched on pilots who give the pertinent details in a concise manner on first call!... So sometimes when you get "dumped" like that it's not to say we haven't tried handing you over, it's just sometimes more appropriate to freecall you over.
Being inexperienced I can understand why you would feel uncomfortable, but the fact you got in to the sky expecting a seamless radar service whilst flying low level, outside control airspace is a little naive. At least you now know to plan a bit more on which units to talk to for your next IFR flight.