Have you tried an different rhythm? I find masmoudi one of the odder ones, as it has a slightly going over the beat feel. Have you tried something like maqsoum or saidi? I find they are simpler as they are more obviously regular (but they may totally just be me and the way I am processing them in my brain. I have to at some point actually beat time so I can see exactly where the beats are to satisfy my musical brain. So I know that musically, masmoudi seems more complex, but I don't know if that translates outside of that frame.).
And I see taxim as a bit like a western cadenza, which is where the soloist improvises on the theme, and can play around with the phrasing. So there is still a beat in that there is a structure, but it is not a repetitive, same tempo beat in the same way. Interesting thought though, can there be music without a beat?
If only there was a music academic to tell us the debate on that one.