As this is going to be quite narrow BW transmission from the bird, you will probably need the PLL type LNB.
Very cheap this days.
Do not worry for the Diseq and other mentioned problems. You will just need to orientate the LNB for the proper polarization.
The LNB original corrugated horn should be enough ti get the good signal.
Making the horn antenna bigger you will just make your antenna beam narrower and you do not want that on the boat.
As you are on the small boat and you do not changing your position so fast during the day, a small arduino board can be enough to azimuth point the antenna to the right direction.
The elevation can be set manually and corrected every while, once a week.
If your boat is heavily pitching or rolling then you may consider making a small gyro setup to point your feed always to the sat using the arduino or raspberry pi.