Reproduction of Stata design of a national multi-staged sample in R survey package

I have a 3-stage stratified sampling design of a national survey. I have a code in Stata to do the weighting, but I struggle to reproduce it with R survey package.

Sampling design is the following. The sampling universe is stratified into 49 strata. Within each stratum, sampling is done in three stages. (1) PPS selection of a precinct. (2) Random systematic selection of a household using random route technique, basically. (3) Random systematic selection a respondent within a household using some Kish technique modification.

There is a Stata weighting code that is assumed to preform well:

svyset precinct [pweight=indwt], strata(strt) fpc(npsu) singleunit(certainty) || qnum, fpc(nhh) || _n, fpc(nhhm)

Here, precinct are precints' numbers, strt are strata codes. Population sizes used for FPC are npsu - number of PSUs (i.e. precincts) per stratum, nhh - numbers of households in PSUs, nhhm - number of eligible members in a household. qnum - questionnaire unique numbers, which are the same for both selected households and respondents.

I try to reproduce it with the following R code.

library(survey)
options("survey.lonely.psu" = "certainty")
svy_data <- svydesign(ids = ~precinct + qnum,
                      strata = ~strt,
                      weights = ~indwt,
                      fpc = ~npsu + nhh,
                      data = data)

I can't do fpc = ~npsu + nhh + nhhm, because than I get an error:

Error in popsize < sampsize : non-conformable arrays.

Resulting confidence intervals through "confint(svymean(...))" in R doesn't match with Stata confidence intervals through tabout ado package. They are close, but shifted a bit in R.

My assumption is that I should do something that Stata's _n term does, and get a 3-stage design instead of a 2-stage one. How could I do that?

Or is there anything else I can try to improve in my R code to match Stata?