Zero-inflated Poisson: ratio (95% CI) for a 0,1 variable

I would greatly appreciate advice about the best way to calculate the overall ratio and its 95% CI (not the difference) for a categorical variable with values 0 or 1 in zero-inflated Poisson regression (zip) in Stata/IC 16.1. For example, in the fishing dataset, calculate the overall ratio and its 95% CI for the number of fish caught for camper=1 / camper=0 given that campers who go fishing catch more fish than non-campers who go fishing (count model) and campers are more likely to go fishing than non-campers (inflate model):

Code:
use https://www.stata-press.com/data/r16/fish
zip count persons child i.camper i.livebait, ///
inflate(persons child i.camper i.livebait) vce(robust) irr nolog
Zero-inflated Poisson regression                Number of obs     =        250
Nonzero obs       =        108                  Zero obs          =        142
Inflation model      = logit                    Wald chi2(4)      =      31.53
Log pseudolikelihood = -712.4109                Prob > chi2       =     0.0000
------------------------------------------------------------------------------
             |               Robust
       count |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
count        |
     persons |   2.307947   .4018602     4.80   0.000     1.640645    3.246663
       child |   .3070827   .1140441    -3.18   0.001     .1482986    .6358779
    1.camper |   1.816776   .6923589     1.57   0.117      .860826    3.834313
  1.livebait |   6.164537   2.812036     3.99   0.000     2.521236    15.07258
       _cons |   .0861211   .0717259    -2.94   0.003      .016834    .4405871
-------------+----------------------------------------------------------------
inflate      |
     persons |  -.9311615   .2235628    -4.17   0.000    -1.369337   -.4929864
       child |   1.958577   .3640051     5.38   0.000      1.24514    2.672014
    1.camper |  -.8716704   .4055473    -2.15   0.032    -1.666529   -.0768123
  1.livebait |   .7407971   1.512794     0.49   0.624    -2.224225    3.705819
       _cons |   .8337162   1.751823     0.48   0.634    -2.599794    4.267227
------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline incidence rate.
 
. mchange camper, stat(all)
zip: Changes in mu | Number of obs = 250
Expression: Predicted number of count, predict()
       | Change p-value LL    UL    z-value Std Err From  To
-------+-------------------------------------------------------
camper |                                                                                       
1 vs 0 | 2.153  0.022   0.314 3.991 2.295   0.938   1.840 3.993
Average prediction: 3.230
 
. * Ratio camper/non-camper
. di 3.993/1.840 = 2.1701087
. * Lower 95% CI
. di (1.840 + 0.314)/1.840 = 1.1706522
. * Upper 95% CI
. di (1.840 + 3.991)/1.840 = 3.1690217
 
. margins camper, post
Predictive margins, Number of obs = 250, Model VCE : Robust
Expression: Predicted number of events, predict()
------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      camper |
          0  |   1.839983    .518668     3.55   0.000     .8234123    2.856553
          1  |   3.992508   .8026569     4.97   0.000      2.41933    5.565687
------------------------------------------------------------------------------
 
. nlcom (Ratio: _b[1.camper] / _b[0.camper])
  risk_ratio:  _b[1.camper] / _b[0.camper]
------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  Ratio      |   2.169862   .7368881     2.94   0.003     .7255876    3.614136
-------------------------------------------------------------------------------
Using mchange (from SPost) I calculate (above) that the camper/non-camper ratio (95% CI) is 2.170 (1.171-3.169), p = 0.022. However, nlcom (above) returns 2.170 (0.726-3.614), p = 0.003.

The Stata Base Reference Manual Release 16 entry for nlcom on page 1721 (Technical note) says in part, ‘The test of H0 : exp(β) = 1 is asymptotically equivalent to a test of H0 : β = 0, the Wald test in the original metric, but the latter has better small-sample properties. Thus if you specify eform, you get a test of H0 : β = 0. nlcom, however, is general. It does not attempt to infer the test of greatest interest for a given transformation, and so a test of H0 : transformed coefficient = 0 is always given, regardless of the transformation.’

1. The Reference Manual entry suggests that the mchange estimate may be better than the nlcom estimate. Is that correct?
2. What is the best way to calculate the 95% CI of the ratio of campers/non-campers?