Help with interpreting Linear Mixed Models - ignore p-value, just go on B-estimate?

I have been given advice that I should always interpret the relationships shown in the model of best fit, from having run a linear mixed model, regardless of the p-value.
I want to do this anyway, as some of my moderator/predictor variables didn't quite reach significance.
But I know my examiners are less familiar with these analyses and are used to just going on p-values.

Could someone find me a reference, ideally a journal article, that explains why using the B-estimate (i.e. change in slope) is better than using p-values and effect sizes, when interpreting linear mixed models? I get it gives better real world info, (i.e. for a unit increase in X, we see an [estimate value] increase in DV, for each unit time). But what's the evidence to say this is a relationship we should accept, when the p value is greater than 0.05?

Many thanks!