What is the best Optimizer for sites running the "Membership" plugin?

I’m having a serious issue with the dreaded ‘white screen hang’ in between page and post clicks on my site. I used to use WP-Optimize and/or WP Database Cleaner but they don’t help with innoDB structure which I believe is used by the ‘Membership’ plugin.

I have exhausted all other possibilities when it comes to fixing my white screen issue and all I’m left with is a potential corruption in my Database which means I either need to find a fix or scrap it down to nothing and start again.

Any insights to this problem would be seriously appreciated…