i2c not really accessible in the open source fpga workflow. It requires a lot of software overhead, you would have to instantiate a CPU then write a driver to handle it. It looks like analog devices has a lot of other analog to digital encoder options:
I would pick one of the ones with the “pixel bus” ie parallel outputs. ADV7181D looks pretty nice.
The TVP5150 may also be workable, not familiar with the output video standards it references.
The FPGA is sort of a brute force solution. Writing a driver for a two wire interface like i2c (that usually comes for free in microcontrollers) is actually really hard. However devoting 36 pins to a parallel bus from a 381 pin chip with 180 or so gpio pins is easy. Anything that can be done in parallel is better, serialization is hard (all opposite of microcontrollers).
It may also be possible just get tough and write a decoder core for verilog but that sounds like a pretty serious project on its own.