You can't purchase hdmi transmitter components unless you're a HDMI adopter (See https://www.analog.com/en/products/adv7535.html)
I agree with you on the DVI-I. As shown on the architecture bloc diagram I propose, I plan to implement DVI-I as a first step (https://www.patreon.com/posts/motherboard-v-47744392). It will output the same signal than HDMI but it will not embed the audio signal.