We have implemented several fast and flexible adaptive lapped orthogonal transform (LOT) schemes for underdetermined audio source separation. This is generally addressed by time-frequency masking, requiring the sources to be disjoint in the time-frequency domain. We have already shown that disjointness can be increased via adaptive dyadic LOTs. By taking inspiration from the windowing schemes used in many audio coding frameworks, we improve on earlier results in two ways. Firstly, we consider non-dyadic LOTs which match the time-varying signal structures better. Secondly, we allow for a greater range of overlapping window profiles to decrease window boundary artifacts. This new scheme is benchmarked through oracle evaluations, and is shown to decrease computation time by over an order of magnitude compared to using very general schemes, whilst maintaining high separation performance and flexible signal adaptivity. As the results demonstrate, this work may find practical applications in high fidelity audio source separation.