Has anyone been noticing some odd crackling or static when some sound effects play in the game with the default DOSBox? I'm on Windows 10 64-bit 1803, by the way.

I do, I have the same problem. I'm also on Win10, latest version.
While the music is fine, the sounds are blaring and heavily distorted (to the point of those EARRAPE troll videos).
I wonder why because many other DOSBox games I play do not have this...
Maybe something faulty with the SB emulation?

I need to find something to record first but I can give it a try, I'll let you know ASAP.

Did anyone end up solving this? All of a sudden the audio in the main menu sounds distorted and the music isn't playing right. Using DOSBox-X, tried general midi, Sound Blaster, no difference.

I used to have this exact problem and tried to run Tyrian 2000 with different forks of DOSBox, and with DOSBox ECE it sounds perfect. So I compared the 'conf' files from both versions and it looks like the difference in the Mixer settings is the cause for these issues. You can edit the game's 'dosboxT2K.conf' and 'dosboxT2K_setup.conf' and change to DOSBox ECE's settings:

GOG DOSBox Mixer Settings (original settings)

[mixer]
blocksize=2048
prebuffer=10

DOSBox ECE Mixer Settings (change to these settings)

[mixer]
blocksize=1024
prebuffer=25