I agree with DocV that (4) is the only sentence of the bunch that works. "Let alone" doesn't work in the first three sentences. I think "not to mention" would be a decent replacement in (3), provided you delete "the" in "the money."
(3a) Carrying out this research project will require a lot of time and effort, not to mention money.
The reason "the" doesn't work there is that "not to mention money" is short for "not to mention a lot of money." In (1) and (2), it is harder to find a replacement phrase for "let alone." I think "what to say of" might do the trick, but it's a stretch:
(1a) Here we have but a limited selection of his paintings, what to say of the works of other members of his group.
(2a) We present here only a limited amount of the research our own team has carried out, what to say of the research by other groups.
I'm preserving the red coloring because I'm not entirely comfortable with the substitution. I don't think I've used "what to say of" in that way in my own writing. If you're concealing what's natural here, Navi, please do unveil it. I give up.
Please note I also added "but" in (1a). Its function parallels that of "only" in (2).