[blimey]

Batch mode in IDM is a good choice.

In IDM; Tasks, Add batch download.

Enter URL with asterisk for variable, for example;

h..p://cdn.be-at.tv/001460/128/1250/*.beat

And set wildcard size to 4. For "From" enter 0, for "To" enter number of last file, like 200, 500, 1000, or whatever it is.

No "missing audio for a few ms" (or any missing audio whatsoever) when using ffmpeg here. And I've done several sets now.
But, we've been down that road already...