My observation, based also on @deebzzz’s comments, is that the problem in Elite is affected by the resolution. It does however appear more complex.
On a 2070 Max-Q on 1080p using 0.65x “supersampling” (Frontier’s own “normal”, but also with equivalent in rendering resolution FSR modes) Elite seems to be able to run for at least an hour. Granted, I only tested it AFK in a station, but stations tend to be on the heavy side in Elite (a settlement might have been admittedly even better). At the same time, on a 3080 12 GB, likewise on 1080p, it seems stable even with supersampling of 1.0x. But I haven’t tested this extensively—I just know that 2.0x produces the Xid within seconds, and anything above 1.0x tends to trigger it soon as well. It is possible that with 1.0x it just needs more time. Still, on the 2070 Max-Q 1.0x does trigger the Xid 13 almost immediately, so there is a difference. Whether this is due to VRAM size or GPU architecture, I can only be guessing.
This obviously provides a workaround: try lower settings for the supersampling option (or whatever it was specifically called) until one is stable enough. Considering Elite’s abysmal AA, I don’t find 0.65x to be that much worse compared to 1.0x. Not being able to use 2.0x, however, is frustrating, because 2.0x does mitigate these aliasing problems by a considerable degree.