There is no such thing as "not removable".
There is only "not removable yet".
I've had this approach since a was about 6 years old, when looking at something:
Well somebody put this together
That means I can take it apart
The guy that runs the Vintage Kustom forum actually removes the internals, and the wood baffles...then he takes them to a self serve car wash, and hits them with the power washer. For real.
Remove the speaker, and...
Mix water with this...
View attachment 14172
In one of these...
View attachment 14173
Apply firmly, but gently with one of these(a soft one)...
View attachment 14174
Use one of these...
View attachment 14175
With one of these on the end of the hose...View attachment 14176
To suck up the loosened funk.
Easy-peasey.