I don't think bootstrapping solves the problem. If your data doesn't comply with your model assumptions (Normal distribution of response), you should search for a better fitting model. Typically, this assumption is violated, because your response variable has lower bounds (e.g. zero). In such a case, you can better use a Generalized Linear Model. Read the full story here: https://schmettow.github.io/New_Stats/glm.html#elements-glm.

Furthermore, I'd be careful with clinging to APA standards, especially the use of p-values is outdated (see here: Article Moving to a World Beyond “p < 0.05”

You don't necessarily need normally distributed data for linear regression analysis. The key assumptions are actually about the residuals, which should follow a normal distribution. This requirement holds independently of the overall distribution of the data. It is also important to check for collinearity between variables, typically done using the variance inflation factor. Adequate Durbin-Watson values are also essential to ensure independence of residuals.

Bootstrapping is a robust method that can address various issues. Another way to assess model relationships is by comparing the root mean square error (RMSE) before and after resampling, although SPSS might not offer this analysis.