The reason there's no "original X-Com1 DOS music" out there is:
1. It's an old music format not playable in modern media players.
2. It's virtually the same as the MIDIs in the Windows version.
3. OpenXcom already plays the original DOS music if it's available anyways.
The only reason it sounds different is because DOSBox emulates the old-timey SoundBlaster sound, so the only way to get that effect into OpenXcom is to
emulate the old sound or, like you did, record the music from DOSBox and use that.
We probably can't include it in OpenXcom directly but feel free to post it here for other players to enjoy.