The monthly is a good idea.
It's just how to promote it.
With the weekly comp you have to make an effort to submit and then you get interested in the outcome. Even if you don't enter you still tend to have a look.
With the monthly - your entry is via winning the weekly - so not as much chance to enter - hence not as much click through.
How about including the 'best runner up' to the entrants, that way just because you haven't won - you may still get in so might be inclined to come and have a look to see if you made it.
I could also suggest having a quarterly comp made up from monthly winners with best runner up which in turn leads to an annual comp with the 4 quarterly winners plus best runner up.
I put this suggestion forward so it might start with January if there is any interest.
If you have a chance of winning pic of the year - you will have an all year interest in what is going on!