A general comment might be useful. These discrepant significances for unstandardized and standardized coefficients seem to happen when a linear model is not suitable in the first place. Examples include a DV with a strong floor or ceiling effect and a DV that is multimodal.
For my PhD research, I am running a model composed by 10 latent variables, in which I want to estimate the direct effect of 9 independent variables to my dependent variable, and also want to estimate one mediation effect. For estimating this mediation effect, I run the bootstrap. My dependent variable is categorical (and has also a skewed distribution), so I used the WLMVS estimator. Therefore, for writing the paper, should I use the standardised or the unstandardized results for reporting the direct effects from all independent variables to the outcome variable, and also for reporting the indirect effect? Many thanks in advance for your help