You have to not include the Sent program status on the send flow because exactly what will happen will happen. better to have a Delivered flow listening for the Delivery/sent and then marking the full executed lead.
For the smart list, you can exclude a suppression list, but Communicaiton Limits aren't calculated until you run the campaign.
The way to turn off the limits is to go to the Admin > Communication limits, or bypass this on the Schedule tab at the bottom: Ignore Limits.
If you can't do that, then you don't have access and need to ask your Admin.