But my humble understanding, which I am sure you will correct should I err, is that the government (GC) supports the opening of the Ledra street and the increased interaction between the communities.
Yes this is correct. The government supports the opening for the reasons you said. Unfortunately such opening would also bring the problems I mentioned above (which is what Turkey was aiming for) that I mentioned above.
For me, as an outsider, I see no other way, in fact. Only increased interaction can soften both fronts enough to pave the way for a solution.
Personally I disagree. Interaction is only one of the components needed for a solution. The other major requirement for a solution is an understanding that no side can gain on the loss of democracy and the violation of the human rights of others.
This understanding does not come from interaction. Human greediness is not voluntarily abandoned. (otherwise societies would not have such a big contrast between rich and poor). This understanding comes when you realize that your greediness actually makes you worst off than better off as you hoped it will.
And in fact, I have the impression that the merchants in the South stand to profit more from the opening than those in the north. TCs are much more likely to cross to the south to purchase goods not available, be it because of the size of the market or economic restrictions, in the north. In fact, I know of no one who has not crossed (who is allowed to).
This is a wrong impression. The opening of the gates had a major positive impact on the standard of living of Turkish Cypriots while it had no effect (probably a negative one from a financial perspective) on Greek Cypriots.
An amazing number of GCs, though, have not visited the northern part of their hometown
I am from Limassol. If part of my town was illegally occupied and I had to show a passport to visit as tourist my own home I wouldn't do it either. Not to mention that entering the occupied areas you enter a land that laws can not be enforced and we would be on the mercy of the occupation army. (which is why the occupied areas are full with fugitives from justice)