You’re right that the basic monthly samples do not include replicate weights. For most analyses with the basic monthly data, just weight your analysis using WTFINL. There is no cluster or strata information in the data. Keep in mind that since this is a complex survey design with clustering and stratification, but information about the design is not available in the public use microdata, the standard errors will be estimated with bias (with uncertain direction). IPUMS testing has found that using replicate weights with ASEC data usually increase estimated standard errors slightly. So your standard errors are likely to be slightly underestimated.
If you are using the CPS data longitudinally, there are a separate set of weights created by IPUMS that can be used in your analysis. More information on those is here: https://cps.ipums.org/cps/cps_linking_documentation.shtml#linked_weights