This route seems to be a mystery even to locals in all towns involved… But here is what we did, and we got there (nearly didn’t, nearly died, but we got to Guatemala).
First catch the Hokey pokey ferry to Independence. leaves from the M&M gas station in the center of town. Two times in the morning available 6:45am, and 7:45. (12 minutes, 10 BZD)
There was rumored to be a 8 am bus from independence to Punta Gorda, there was also rumored to be a 9 am bus, even according to the James bus line, but either it was late or it is really 9:30, because our bus showed up at 9:30 am (1.5 hours, $9 BZD)
We found most buses in Belize to be surprisingly on time, so maybe it was actually 9:30am, but still it is best to check. If you come through Dangringa ask there, this info is probably as good as it gets.
After you depart the bus you need to first buy your ticket for the ferry to Livingston (Puerto Barrios also available) once you have your ticket you need to got and take care of your Belize exit fees and get you exit stamp. ($37.50 BZD exit per person)
There are a few boat lines that go to Livingston typically only on Tuesdays or else you take a boat to Puerto Barrios and then Launchas back to Livingston.
If you plan to do it on a Tuesday the cost is$60BZD at “Memos” boat. (45 minutes) His boats are in rough shape, I don’t know about the others but we sat for 10 minutes in a thunderstorm while they were cutting and splicing wires to jump start the motors.
If it wasn’t pouring and the only option I probably would have gotten off. Boat times are rumored to be 10, 11, and 1pm. We took the 1pm that left at 1:45pm with smoke and sparks coming from the battery.