WTFINL is the correct weight to use for (un)employment estimates by occupation and the weight should be divided by the total number of months in your analytical sample.
The approach for strata identification you have outlined is consistent with the recommendation from Davern et al. (2007). I will note that when using the smallest identifiable geographic unit (PLACEFIPS) as the stratum, many households will end up in the STATEFIP remainder. You might therefore add COUNTY as an intermediate stratum identifier. Households without an identified PLACEFIPS but with an identified COUNTY get their own stratum and only those with neither would fall back to state. Note that PLACEFIPS should always be combined with STATEFIP to uniquely identify cities. Additionally, in a cascading approach like this, it may make sense to restrict strata to only COUNTY and PLACEFIPS codes that appear across all vintages. A code that gets dropped or added later splits the same area across the three tiers, which can leave a stratum with too few PSUs and understate the error term. Since PLACEFIPS codes (in combination with STATEFIP) are unique across vintages (i.e., the same place should have the same code across vintages), there is no change in codes over time that needs to be accounted for.
On the choice of PSU, I would revise my recommendation and suggest using the unique household identifier CPSID rather than YEAR + MONTH + SERIAL in order to incorporate the rotating panel structure of the CPS. This adjusts intervals for the repeated sampling that you have noted.