I would like to replicate the BLS's computation of labor force statistics.

I do not think that IPUMS has the correct variables for weighting these surveys. For example for the basic monthly surveys, what is apparently needed is

CPS (Basic) Weighting Variables: PWCMPWGT Jan 1994 - current Weight-composited final weight

These weights do not appear to be in IPUMS-CPS. Thus WTFINL (the IPUMS final weight) for the basic monthly surveys) is not the same as PWCMPWGT. Nor does WTSUPP yield the right results for the March surveys.

You are correct that IPUMS-CPS does not currently offer a PWCMPWGT equivalent variable. The variable WTFINL generally corresponds to the original CPS variable PWSSWGT which is used for most tabulations. You can attach PWCMPWGT to non-March IPUMS-CPS files from their corresponding NBER raw CPS data files using the method outlined in the answer to this question.

PWCMPWGT is generated for the Basic Monthly data files. Because the March Supplement is special in that it includes an oversample, the March Basic file and March Supplement file are considered separate. IPUMS-CPS does not currently offer the March Basic files and the March Supplement file does not contain the PWCMPWGT. Instead the IPUMS-CPS variable WTSUPP corresponds to the variable PWSUPWGT and is the primary weight used for the March Supplement sample.

I hope this helps.