One more thought on this: Your help text talks about data-driven block sizes which are in the range 4 ... 13. So maybe sizes of 2 or 3 or not very interesting or meaningful anyway? Or to put it differently: What happens if you choose the recommended block size for the sample size, and then vary that size a little bit? If this still changes the results (confidence intervals) a lot, then maybe that's more problematic.

I have no idea whether this functions is actually implemented in some other language...

Don't know, but it seems that for their paper (https://arxiv.org/pdf/2205.00577.pdf) those Gao, Peng and Yan guys have implemented it somehow, for comparison. Haven't seen any code offerings, though.

Anyway, they write "It seems that the MBB method always generates a CI larger than it should be", so perhaps your latest result of having a wide band (although not so wide as before) is in line with that.