Consequences of CMC(ℵ0,∞) or cf(ℵ1)=ℵ1 for P-space properties at uncountable κ

Determine whether either CMC(ℵ0,∞) or cf(ℵ1)=ℵ1 implies, for every uncountable well-ordered cardinal κ, that (a) both S_{P}(κ,[κ]^{≤ω}) and 2^{κ}[[κ]^{≤ω}] are P-spaces, or (b) S(κ,[κ]^{≤ω}) is a P-space.

Background

Building on Theorem s5:t6, which shows certain implications from stronger assumptions, the authors highlight that it is currently unknown whether either the countable multiple choice principle CMC(ℵ0,∞) or the regularity of ℵ1 alone suffices to force the relevant P-space properties at all uncountable well-ordered cardinals κ.