You're making the argument that Solomonoff induction would select "the sun rises every day" over "the sun rises every day until day X". I agree, assuming a reasonable prior over programs for Solomonoff induction. However, if your prior is 99% "the sun rises every day until day X", and 1% "Solomonoff induction's prior" (which itself might assign, say, 10% probability to the sun rising every day), then you will end up believing that the sun rises every day until day X. Eliezer asserted that in a situation where you assign only a small probability to Solomonoff induction, it will quickly dominate the posterior. This is false.

most of the evidence given by sunrise accrues to "the sun rises every day", and the rest gets evenly divided over all non-falsified "Day X"

Not sure exactly what this means, but the ratio between the probabilities "the sun rises every day" and "the sun rises every day until day X" will not be affected by any evidence that happens before day X.