Ciao Roman,
I recall reading your review of the Baby Twin with interest. I used to have a Starbucks Sirena, which used a similar boiler + thermoblock setup (the former for brewing, the latter for steaming). The low-quality "wet steam" I was getting had nothing to do with the stock Gaggia-style wand, but rather the thermoblock. My workaround consisted of preheating the block at least 3 times before steaming the milk; that meant switching to steam mode, then off (back to brew mode), then on again (to steam mode), quickly & repeatedly, to put as much heat into the thermoblock as I could, within reason.
Since I don't have a Baby Twin or its manual, I can't say if you can devise a similar workaround. But I suspect the same principle holds in your case: the thermoblock will make stronger steam if it can just get hot enough. Mind, though, this is still not a perfect solution; even with preheating, the stronger steam does not last long, 30-45 seconds at most. I found the best way to make use of it is to steam just enough milk for one drink at a time, using a small (12 oz.) pitcher.
Note: I upgraded partly because I wanted better steam, so I could make 2 cappuccini at once. Sometimes upgrades have a social benefit.
Buona Fortuna,
Wayne