I know that both Kalmia polifolia (swamp laurel) and Kalmia angustifolia (sheep laurel AKA lambkill) will grow in wet soil or even part-time very shallow water. IME both are smaller and less ornamental than Kalmia latifolia, mountain laurel, but mountain laurel likes moist well-drained soil. I think if your site is too wet for rhododendrons, it will also be too wet for mountain laurel.

Anyone have any suggestions of an evergreen flowering shrub max about 5' (3' size would be nice) that can handle somewhat wet soil?

Mountain laurel requires excellent drainage, another way of saying lots of oxygen around the roots, even more than rhododendrons do. There are evergreen hollies that will grow under very damp conditions. Some leucothoes and lyonia will also. None of these have very showy flowers, but the berries of winterberry holly do add a welcome touch of color in the darkest seasons.

For sure not the mountain laurel. I have lost several to poor drainage in winter. Leucothoes are nice, but probably smaller than you would like. In zone 7 Nandina could work. What about sweet olive, Osmanthus fragrances? It would get taller than 5 feet however. It is one tough and lovely plant.