I’d use OSSC, with output connected to an HDMI capture device.
I can’t see anywhere on the OSSC wiki that says it supports 1024x768 at 75 or 72Hz, which I’d need here. Do you know differently?
I use it with not just my Amiga computers, but also old PCs and the Wii.
As I understand it, it does handle 720p and 1080i input well.
I’ve used 1024x768 no problem, but VGA-style (from my 386), which I believe is 70Hz-ish. I do not know how it handles vertical refreshes over 70Hz, but my guess is that it’s fine, as, same as screens, the clock that matters is the line (horiz) clock (in kHz).
This is the ADC chip used: https://www.ti.com/lit/ds/symlink/tvp7002.pdf
Page 14 has a nice table of resolutions and clocks that are supported for sure. This includes 1024x768 at ~85Hz. I do not know, however, if the FPGA will handle it on the other end of the ADC.
My advice would be, if you can afford one (at around 100€ it is dirt cheap and extremely high value), to just get one and put it to the test. I love mine, and can’t recommend it enough.