As I said, it would take multiple trips. The transports are just there to ensure that your ships grant least one shot off.
In your case, it would take about 5 to 6 (4 if you can get your whole fleet to ge at least one shot off) trips before the shield goes down.
At which point, taking out the missile guard post should be much easier, and after that is down, making the superfort approachable with bombers.
Not saying it isn't a grind, but I am saying it is possible.
The need for this type of strategy is not a problem (a good challenge will make you think about how to approach a problem, rather than just making you do the same simple thing you had been doing all along. It's the number of times you had to so it that can become a grind. (thus tieing back into the homeworld discussions)
I have mentioned in the past that I would like to see a rework of fortresses to be less "hard counter to everything but one class of thing", to help avoid these types of worst case grind.