Anything that is "SIA" is also "SSA," since SIA can be produced by adding on more information.
No it's not. If you add on "you are an observer who is a human", you update with the universes with human observers being more likely. They do work the same if you use different priors. Namely: make universes with more people proportionally more likely in SSA, or less likely in SIA, and just use "conscious observer" as your reference class, and you'd get the same thing.
I still don't see how your method works.
Probabilities come from information. So priors come from your starting information. Which information you label "starting" is completely arbitrary, however - you can't get different answers just by relabeling what you know.
So any problem that you can look at from an SIA perspective, you can also take a step back and look at it from an SSA perspective - it just means labeling less information "starting" information.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.