After looking through some papers, I feel qualified to answer my question, for the record.
The scheme works and I've found no evidence that it has been broken. A good review is given in "A survey of ring signature" by L. Wang, which contains a section on linkable signatures.
The technique used in Liu's 2004 paper from the question makes O(n)-long signatures, where n is the number of public keys. There are more recent schemes commonly called "short LRS", which produce O(1) signatures. However, all schemes that I saw require some kind of trusted party to be involved in the generation of key pairs. This defeats the purpose of LRS I think, and anyway is unsuitable for my applications. From my superficial understanding, in O(1) schemes the danger of chosen key attack is somehow greater, and has to be compensated by including this key managing authority.
As for real applications, I found one (unfinished?) implementation of the 2004 scheme, and that's it.
So I've implemented the 2004 scheme and a similar, but more efficient scheme by the same authors. It's here: https://github.com/sorrge/LSAG . Public domain. Not reviewed by anyone yet, so no promises of its security.