Interpreting and transforming GLM output parameters with a Gamma log link

Question

I built a GLM model in R with a Gamma log link and where my response variable is "1 - effectiveness". I would like to report the results of my model directly in terms of "effectiveness", but I am unsure about how to interpret and transform model coefficients and report them correctly.

I modelled "1 - effectiveness" because this was a transformation requiered to use Gamma. Effectiveness ranges from negative to 1, and therefore "1 - effectiveness" has zero to positive values, and adjust well to a Gamma.

This is my R output:

glm(formula = one_minus_eff ~ theat + resources + governance + 1, family = Gamma(link = "log"), 
    data = dataframe)

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept) 0.146929   1.014147   0.145   0.8861  
theat       0.017819   0.007422   2.401   0.0248 *
resources   0.028103   0.011307   2.486   0.0206 *
governance  1.042097   0.452272   2.304   0.0306 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Gamma family taken to be 0.9350556)

    Null deviance: 46.378  on 26  degrees of freedom
Residual deviance: 29.711  on 23  degrees of freedom
AIC: 257.57

Is this interpretation expressing the results in terms of "effectiveness" correct?:

"For resources, the coefficient is 0.028103. This means that, all else being equal, a one-unit increase in resources is associated with an increase of 0.028103 in the log-transformed "1-effectiveness" (one_minus_eff in R) because family is Gamma with a log link.

However, because the response variable is in log units (due to the log link function), I need to take the exponent to interpret the effect on one_minus_eff in its original units. The exponential of 0.028103 is approximately 1.0283.

So, a one-unit increase in resources is associated with an approximate 2.83% increase in the original one_minus_eff value, assuming all other variables in the model are held constant. This effect is relative to the units and scale of the data and the assumptions of the Gamma family with a log link.

Similarly, a one-unit decrease in resources would result in a 2.83% decrease in "1-effectiveness". I could revert that sentece by changing the sign of the coefficient and claim that the same one-unit decrease in resources is associated to a 2.83% increase in effectiveness."

Is the above logic correct?