If you have enterprise edition of SFDC (I guess you do becuase you have record type) then personally I would always encourage managing this on the SFDC side with the use of sharing rules. The introduction of criteria based sharing rules in SFDC have made this a lot easier than it would have been a few years ago. The advantage here is that you are in control and can modify the rules at any time. With the sync filter on the Marketo side you will always have to reach out to support to make any changes.
Let me respond to your goals (I am assuming that support have at this point put in place a sync filter based on the check box field.)
1. To get everything over you will need to ask support to remove the filter and then ask them to refresh the sync timestamp for the lead and contact objects. I'm not sure you actually need to do this, maybe you have left out a detail, but what will you gain from brinign all records over? Did the initial sync not pull over som records rthat you were expecting?
2. You can create a campaign in Marketo
SMART LIST : email address is empty FLOW delete lead (delete in SFDC = false)
3. To prevent leads with no email addresses in SFDC from coming back to MArketo you can create a criteria based sharing rule in SFDC so that your marketo sync user can only see records where email address is not = NULL. The steps for this are outlined in a video in the MArkeot university, It's the Admn SFDC #2 video.