Overdispersion in a binomial GLMER model

Question

I'm having trouble accounting for overdispersion in a binomial GLMER (lme4 package) - I'd read through other posts on the topic but haven't found anything that solves my problem. I tried adding an observation-level random effect but that resulted in the model not being able to converge.

My data looks like

> str(exp)
'data.frame':   22 obs. of  6 variables:
 $ Indiv        : Factor w/ 22 levels "Cadence","Caesar",..: 1 4 7 8 9 11 12 15 17 20 ...
 $ Sex           : Factor w/ 2 levels "F","M": 1 1 1 1 1 1 1 1 1 1 ...
 $ Mum           : Factor w/ 12 levels "Asha","Hazel",..: 12 10 2 3 6 11 9 5 4 1 ...
  $ joey_number   : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 2 2 3 3 3 ...
 $ No_prev_used  : int  11 7 0 8 12 3 3 8 5 3 ...
 $ No_new_used   : int  1 5 13 8 18 1 4 1 1 4 ...

My model is

bb <- glmer(cbind(No_prev_used, No_new_used) ~ Sex + joey_number + 
              (1|Mum), family = binomial, data = exp)

The response variable is proportion data. This model gives the following output:

> summary(bb)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod
]
 Family: binomial  ( logit )
Formula: cbind(No_prev_used, No_new_used) ~ Sex + joey_number + (1 | Mum)
   Data: exp

     AIC      BIC   logLik deviance df.resid 
   120.9    127.4    -54.4    108.9       16 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.25276 -0.62432  0.05726  0.49615  3.16098 

Random effects:
 Groups Name        Variance Std.Dev.
 Mum    (Intercept) 1.413    1.189   
Number of obs: 22, groups:  Mum, 12

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)   
(Intercept)  -0.39176    0.47697  -0.821  0.41144   
SexM          1.16087    0.48747   2.381  0.01725 * 
joey_number2  0.04535    0.49081   0.092  0.92638   
joey_number3  2.00190    0.61605   3.250  0.00116 **
joey_number4  1.76223    1.07721   1.636  0.10186   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) SexM   jy_nm2 jy_nm3
SexM        -0.500                     
joey_numbr2 -0.295  0.085              
joey_numbr3 -0.405  0.356  0.286       
joey_numbr4 -0.263  0.329  0.190  0.210
> Anova(bb)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: cbind(No_prev_used, No_new_used)
              Chisq Df Pr(>Chisq)   
Sex          5.6711  1   0.017247 * 
joey_number 12.5533  3   0.005709 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Using the dispersion_glmer() function in the blmeco package I am given a dispersion value of $1.42$. The package information suggests dispersion values of $0.75-1.40$ are acceptable. So my first question is, is my dispersion value high enough that it's considered overdispersion (how black and white are those values)? And secondly, if so, what other options are there if introducing a second random factor (observation level) doesn't solve the problem?