Conclusion:
I am in Tanzania now and I have survived the trip which was not difficult at all.
Mike is 100 % right. From Mocimboa da Praia there are quite comfortable busses (the medium size ones) to the border and on to the river. The road did not fulfil European standards and I am thinking of complaining about that to the UN or whoever might be responsible for it. Far away from a suicidal matter.
No hussle at the border whatsoever. The official who searched my luggage did that after we shook hands.
Water was low (therefore I cannot tell how safe it is when the river is high) and we had to take 3 different boat, walking over the sanddunes in between them to cross the next little part of the river.
No hussle on the Tanzanian side either.
Marburg

