I'm in the exact same situation... If LTM gets synchronized my production environment will break. My understanding is that the "Incremental Sync" only syncs the portions that you specifically configure it to sync.
Like with ASM, you can go to Security > Options > Application Security > Synchronize to tell it to sync the ASM portion.
It looks like APM has a simlar feature under Access > Profiles/Policies > Policy Sync
My change got pushed back due to network issues in my environment, so I won't be able to do it for a few more weeks...