Mixed effect model covariance prior

How should I choose the covariance prior for my bglmer model?

This is a model which has the singularity problem.

mod <- Y ~ X*Condition + (X*Condition|subject)

# Y = logit variable
# X = continuous variable
# Condition = values A and B, dummy coded; the design is repeated
#             so all participants go through both Conditions
# subject = random effects for different subjects

summary(model)
Random effects:
Groups  Name             Variance Std.Dev. Corr
subject (Intercept)      0.85052  0.9222
X                0.08427  0.2903   -1.00
ConditionB       0.54367  0.7373   -0.37  0.37
X:ConditionB     0.14812  0.3849    0.26 -0.26 -0.56
Number of obs: 39401, groups:  subject, 219

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)       2.49686    0.06909   36.14  < 2e-16 ***
X                -1.03854    0.03812  -27.24  < 2e-16 ***
ConditionB       -0.19707    0.06382   -3.09  0.00202 **
X:ConditionB      0.22809    0.05356    4.26 2.06e-05 ***


I would like to use the blme package to run the model with a cov. prior. However, there are multiple options to choose from, e.g. wishart, invwishart, gamma and invgamma.

1. What should guide my choice of cov.prior?
2. Is it appropriate to use the rePCA function to check for singularity, i.e. overfitting in bglmer models?
3. Is it appropriate to use the likelihood ratio test with anova function to reduce the overfitted bglmer models?