Well, finally, after about 24 hours, the webhost-move has finalized! (Of course, it depends on local DNS-servers’ cache etc.)
I decided that the deal I was getting from my last host was not good enough, compared with what was available from other companies – so I started searching for a new one a few days ago, and my choice fell on Quality Host Online.
Much better speeds than the previous host, and a much, much better deal price-wise. (Plus the admin control panel is much cooler…… 😛 )