I have good success suppressing moss by leaving pots out in the rain for six months to a year, before planting them. When I'm ready to use them I rinse with boiling water a few times and then let it cool. Moss is a lot less aggressive in well-leached media. I usually don't have space or time to make pots up that far in advance, with the exception of my seasonal temperate divisions, but several rinses with boiling water and one or two long soaks do a good job with only a day or two's turnover. With many plants I don't care enough to bother, but for the smaller ones that are sensitive to moss it helps a lot.
When I see moss or algae getting started I take the pot and rinse the surface forcefully with a spraybottle, tipping the pot to let the crud drain off. If you disturb it while it still hasn't quite formed a mature colony, it will come loose easily. And the biological activity as the remaining algae/moss regrows removes the nutrients in the media that cause the problem to begin with. After a while, it recedes to manageable levels or dies out entirely.
As an example, I had a pot of D. spatulata that I more or less ignored for like three years. The carpet moss between the plantlets grew up so high that their leaves had to climb up to emerge from the moss; some of the plants were so deep that they almost looked more like VFTs or head lettuce, with the tops of the leaves poking out and the growth point wrapped up in younger leaves. The moss smothered several of them before I repotted, but all I did was pull off the layer of moss and put the plants back in the same pot. The peat and perlite underneath is still perfectly good, but the moss seems to have mostly depleted it. So far, no more moss or algae has shown up, but the spatulata seem perfectly happy.
PS - Nice pics Av - I'm definitely jealous of your camera skills. (Equipment?) Also, footnote to your original carpet moss question; I actually plant Utrics in my pots of larger plants to keep pests from growing. For Utric pots, though, I guess that doesn't work.