A mini-split system is a great idea as mentioned, but because you said you don't have the space or desire to go that route, I'll continue with our conversation on the ductwork.
Adding extra 16"x8" will not effect the airflow anymore than the extra lengths of 6" that would be required if the main duct was not extended. It just depends on the lay-out. A 6" pipe will deliver about 120 cfm at .1 static pressure. Length of the duct and supplies will be a factor as well as the number of supplies. I use a round number of 100 cfm of airflow for a 6" pipe. This is a number I use to size the ductwork in my head. Using your house as an example, with the 8 - 6" supplies, I would size the duct to 18"x8". You want to add 3 more, the duct should start at 24"x8". We used to size the supplies (5", 6" or 7") according to the room size, but the cost of all the different materials (sizes) just became to costly.
When you mentioned "tapping", what I have seen is contractors do is to put a tee on a existing supply and then extend to the addition from that point. This doesn't work well. It was a misunderstanding on my part....sorry.