You know, that's very bad design approach, if the software promises broad possibilities but in reality restricts user in such a stupid way. It does not matter how it's "convenient" for somebody to use catalogues, smart collections and filters messing up the folder structure, it's not for me.
Despite that I managed to do what I needed.
At first I tried to look at the .lrcat file with sql tools and maybe merge the data I needed into the fresh catalogue. That turned out such a mess! No wonder LR is so slow anymore. So I found another workaround:
1. Use filter to show all picked photos in your old cat. Export the originals into an empty folder;
2. Use CMD (in Windows) to get the list of all the files in that folder, the command looks like that - dir C:\your_folder /s /b /-c / >C:\fileslist.txt;
3. Than open the fileslist.txt in Sublime Text and do a "search and replace" with regexp - first, to delete full path, \S*\\ replace with nothing, second, replace new lines \n with a space;
4. You've got a list of file names! Now copy it and go to LR, turn on text search (filename > contains) and paste what you've copied. You've got all the "picked" files! Select them all and "pick";
???
5. Profit!
But it's not flawless. The problem is if the names have spaces - "dng 001.dng" would search for names containing both "dng" and "001.dng" independently, that's a mess. Also, if you have duplicating names (if you shoot much you probably do) there's a misstep too. You will need to manually check such things, screenshots help somehow.
Adobe, such things are shame. Seriously.