Oblique rotation is recommended because in reality, it is much more likely that factors are correlated rather than uncorrelated--especially in variable sets that show substantial correlations. See, e.g.,
Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift's electric factor analysis machine. Understanding statistics: Statistical issues in psychology, education, and the social sciences, 2(1), 13-43.
High correlations may simply indicate high redundancy and/or high reliability of the observed variables (factor indicators). For a factor analysis, this is not necessarily a bad thing since the factors are based on the correlations (and account for them).
I think you have two options: one is to delete the variable with the highest VIF figure, it is the one likely causing the collinearity. The second option is to transform the data set using methods like square of, square root of, cubic root of, inverse of, etc.