UV Lightmap-pack don't like trapezoids?

Hi fellow Blenderers. I’ve been trying to do some complex detailed interiors and get them lightmapped.
When I use “Lightmap Pack” option, it forces all quads into rectangles and any trapezoid shapes show stretched textures into those corners.
Is there an option to allow shapes that aren’t perfect right-angles, or do I need to split all these shapes into rectangles/triangles?

Here are some visuals to help explain my problem. Please notice the surfaces at the base of the “building” and also the uneven distribution:-