Hi Tony,
I'd say that option A should be fine. The serial number is mainly of importance between Primary and Secondary nodes to tell the secondary nodes whether it needs to update its records from the Primary. Do keep in mind that if you have multiple Primaries in your DNS system without synchronization between them, you will also work with multiple versions of the zone database and you may not want to work with that for too long.
Another option you can try though; Once you have the listener IP exposed to the outside world, run "nslookup" or "dig" commands to confirm that you get all the information you were looking for. Even though the service will be live, no live traffic will know about it yet. Once you feel more comfortable, it will be easier to switch over to the new system.
Regarding the time it takes to propagate the changes throughout the DNS infrastructure, it depends on how long the records can been cached on intermediate systems. Have a look at the TTL values in your Public registrar to get an idea of that. If the TTL's were set to a long time (e.g. 1 hour or 24 hours), you could also temporarily reduce the TTL beforehand to speed up the switchover when it is time for it.
Lastly, if you go for option A and add the F5's listener IP as a 3rd NS to the records, be aware that it is normally up to client/LDNS to decide which one of the three it actually picks and as such it's hard to predict how much traffic will actually hit the F5 listener IP once added.
There is a lot to keep in mind though when it comes to DNS due to it intricate communication between systems. If in doubt, I'd recommend letting someone have a good look over the full DNS infrastructure and then decide on a migration plan.
Hope this helps.