General aviation pilot inadvertently encroaches on a restricted area.

Narrative

Departed HEF on a SFRA VFR Plan. Upon leaving the Washington SFRA; I requested (and Potomac granted) radar service VFR flight following. I climbed to 3500'; and proceeded to fly toward my destination using my IFR-certified moving map panel GPS (Garmin 430) to fly a route around the Demo MOA; the Hill MOA; and R6601. At one point; Potomac Approach asked me to contact another sector. I entered the frequency; and realized that he had just reassigned me to his frequency. I tried to raise him 3 times - the first was no later than 15 seconds after he made the assignment - without success. I proceeded to fly the route; remained on the assigned squawk code; and circumnavigated north and East of Hill MOA and R6601. I saw what appeared to be the river on my right side; though it was quite hazy at dusk. According to the GPS; I was clear of R-6601. I do not know the sector boundaries nor the frequencies used by Potomac Approach in that area - the VFR chart shows contact frequencies for the Class B and SFRA areas. As I began a descent into my destination; I squawked VFR and made a call on the approach frequency listed on the approach chart. At that time; Approach indicated that he'd been looking for me for 10 miles. I allowed as how the previous controller gave me the wrong frequency and had not acknowledged my request for correction. I was given a phone number to call. Once I was on the ground; I contacted Potomac by phone; and was passed to a supervisor to provide information related to a possible violation of R-6601. I provided the information; and expressed my concern about the radio hand off as I would have had the controller as a 'second set of eyes' had I been given the correct frequency. While I was on the phone; the supervisor learned from the range officer that the area was cold at the time of the alleged violation; and advised me that no violation occurred. I thanked him and asked him to look into the hand off issue. Factors: Incorrect frequency information given by ATC; my reliance on the GPS unit to fly close to the R-Area (did not fly enough extra distance to allow a determination beyond a shadow of a doubt); and my failure to call ATC on 121.5 to see if I could get a correct frequency. While I believe I did everything 'correctly'; I usually leave ample distance between a restricted/MOA/alert area and my flight path. A review of the radar tracks will show that I did this for the flight. I am still surprised to learn of a potential penetration into R-6601; but I may have been closer than normal tonight in a desire to reach the destination before the haze got worse. As an added factor; I was seeing lightning strikes within 50 NM of my route; and I wanted to get on the ground and get updated weather from FSS. In the future; I'll leave a wider berth to R-areas and not rely as much on the GPS unit display. I'll also look for alternative communication methods - especially around the DC area - such as 121.5 when flight following hand off goes bad. At the same time; I will consider filing and flying IFR on ALL flights; even short ones; to avoid this circumstance in the future.