Snap to guides while using a constraint eg shift

It seems to me you want to constrain, constrain to snap to.   I think you need to do that in two steps.  Move the object transform till it snaps to your guides then press and hold shift and drag  corner to not snapped to a guide

That is what I wrote you seem to want to double constrain transform you want it constrained transform to snap to guides and to constrain the transform aspect ratio to the current aspect ratio.  I believe you can not do that you may move the transform to snap coroners to one or two guide line then constrain the transforms aspect ratio. I do not think it is possible to have two constraints imposed on transform at once. It like ask you to pat your head with one hand and rub your stomach in a circle with your other hand while one of your hands are tied behind your back.