Ha! So true... and even harder with some songs that others... Some songs I can sing from the first go... but...
I took me months to be able to play the strum part of David Bowie's "Heros" and sing at the same time... there is something really off about how they fit together that is hard to master... try it if you don't believe me!
I Scare Myself by Dan Hicks was a similar experience...
I was a singing bass player before I came to the ukulele, and it took me YEARS to disconnect me fingers and my voice. And yet, even with all that head start...
I am, it appears, a slow learner.
Hopefully it will come easier for you as your journey continues!