HDCD is not really "20-bit audio in 16 bit CD-DA", it rather is some strange filtering / compression / variable gain / soft-clipping thing wich "simulates a SNR of about 20 bit".
It's crap and placebo.
There is a tool out there (hdcd.exe, google for it) which can input 16-bit CD-DA WAV files which have HDCD encoded in their LSB and outputs a 24-bit WAV file (padded to 20 bit).
I tried this some years ago with some HDCDs I own and in almost every case this resulted in odd gain changes in the beginning of the songs, sudden "compression" effects on loud passages etc.
I cannot exclude that the tool has a bug. But actually a wealthy "common sense" tells you that it is mathematically impossible to "encode" 24-bit or even just 20-bit SNR in a 16-bit stream without applying some sort of
a) non-linearity (comparable to A-law or u-law audio used in telephony, that uses an 8-bit non-linear quantization)
b) noise filtering (to simulate a better SNR)
c) adaptive compression or amplification. (as used e.g. in the NICAM audio standard seen in UK's analog TV broadcasting)
So, just forget it.
Better burn your 24 bit FLAC files to DVD-VIDEO or DVD-AUDIO. Both support it natively, as long your player does.