How do you mount a beam under another without using joist hangers or anything that adds thickness? Can you screw it in at an angle from above or below? It's the lower beam that needs to be mounted. Joist hangers will be used on the backside.
Place a piece of regel under each screw regel. Screw the new regel into the regel pieces and also up into the regel above. If it will be visible from the side, bevel the rear part of the regel pieces so it looks planned.