So I can replicate the effect for both the scenarios you describe using my usual 'loop-closure survex' in therion.ini. If I switch to 'loop-closure therion' then both scenarios give co-incident stations 1a and 1b, which I believe is what you are after.
Oh! That's weird. Survex calculates it correctly when I use it in a Survex file with separate begin/end sections, so I don't think the bug is there (but maybe Therion puts it into a certain structure that confuses Survex).
Perhaps Olli or Wookey might have some insight into why Therion gets it wrong when using Survex for loop closure...
I have worked out (I think) what Therion is doing wrong. Only the values in the last centreline section get used for the fix of a point that appears in multiple centreline sections. So in my demonstration, it uses the last three, and not the first one, for fixing point 1b. This could be because when using Survex, it is processing the centreline blocks in reverse order, and either issuing a "*solve" command between them, or just taking the result as a non-modifiable result (so it ignores it when the next centreline block tries to modify it). Eg. this could happen if it is considering each centreline block individually instead of all at once. That sounds like a recipe for hidden faults like this, so I do hope it is not something fundamental in the way Therion handles things. I also wonder how many other things will be secretly ignored. https://github.com/therion/therion/issues/269