I will join longneck, you need to give to give this one to a pro.
If you do not understand about back-feeding a circuit, already, it is too easy to kill someone. I say this without exaggeration.
The biggest problem with running a generator with a transfer switch is that you have to wire it into your main panel.
For basic protection of life, (as well as the law,) it must NOT be possible to have your generator and the power to your house on the same wire, at the same time.
This is not a case of, just for a few seconds, or I would not do that, or I will triple check a written list.
It must not be possible under mechanically, electrically, on with quantum physics.
The reason is that if you put power on the 'dead' wires to your house, it is possible to kill someone a mile away, or more.
Emergency workers expect down lines to be dead. Yes, they do check first, but that does not mean that the situation can not change while they are working on them.
Transformers work backwards, low voltage at your generator (240) quickly becomes high voltage (thousands).
And sometimes people, and pets, or cars, just do not even see a fallen power line.
This is a case of some money to a pro vs life.
Why are you using the LOAD terminals? You have no idea what they do, but what you do know is the GFCI is a different type of thing and the screws are even differently labeled. I am just mentioning this because mains power can get people hurt or burn your house down. "Not knowing" should make you more reluctant to experiment.
Pull the GFCI out of there, cover both the LOAD terminals with tape, and don't use them. Now your project has a chance of success.
That will create another problem to solve, and the answer is "pigtail".
Best Answer
You could use one contact, two, or all three.
If using more than one, you could put them in parallel to reduce amperage through each one, which would increase service life (however if any stick "on", you cannot turn the device off). Or you could wire them in series for a higher capacity to interrupt voltage (but if any stick "off", you cannot turn the device on). The latter is a better fail-safe.