How to address a breach of homogeniety in a one way IG ANOVA

Can someone please clarify:

If I run a Levene's test in SPSS on my data and the result shows a breach of homogeneity (p=0.00), can I reduce the alpha level to .025 to reduce type 1 error, and continue reporting on the new results (post-hocs etc), even if the new Levene's output with the reduced alpha doesn't show any reduction in the breach (i.e Levene's is still p=0.00)?

I have inspected the data and it all appears normal, outliers, skewness and kurtosis-wise, with even sample sizes and 40 people in each sample. I don't believe transforming data or doing a non-parametric test is necessary.

Would appreciate any and all feedback!!

Thank you, Bree