I have almost exactly the same problem with my Yamaha RX379. I’m able to only get an intermittent image from the Dreamcast in VGA mode. 480i content is so far a non starter and subsequently so is 240p. What confuses me though is that I thought 480i content was line doubled to a progressive output, so why would the Dreamcast work with a 480p output but not the line doubled output of 480i content from a PS2? I wonder if a line x2 mode for 480/576i content would solve the problem. My TV does seem to accept the 480px2 mode when connected directly.
Linex3 mode for 240p content might work for you; definitely worth a shot if you haven’t tried so already.