Moiré interfaces host interesting physical states and create a platform for band engineering. Most research to date has focused on the moiré interface of identical lattices. While the continuum model of most common systems, such as twisted bilayer graphene, is derived around zero twist angle, highly non-trivial twist angles are found, at which multiple electronic degrees of freedom experience simultaneous moiré reconstructions for the combination of square and rectangular lattices. This effect is leveraged to find band structures with second-order hybridisation even in the lowest-order continuum model. Additionally, flat bands formed near socalled geometric magic angles are identified. Furthermore, the effect a moiré reconstruction has on the topological phase diagram of the proximity effect between a strong topological insulator and a BCS superconductor is examined.