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zero-inflation beta or gamma model?

Your model is very complication in terms of the random effects. 
Besides...I am not a fan of using year and month as random effects.

As to the zero inflation aspect of the beta GLMM....apologies for 
self-citing here, but Chapter 16 in this book:

http://highstat.com/index.php/beginner-s-guide-to-zero-inflated-models

has a fully worked out example using the zero-inflated beta GLMM with 
2-way nested random effects.

And Chapter 23 in Volume II of this one

http://highstat.com/index.php/beginner-s-guide-to-regression-models-with-spatial-and-temporal-correlation

touches on zero-inflated beta GAMs with spatial correlation and barrier 
models.

Kind regards,
Alain
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