I see I'll have to do the rest of the diagrams and maths before I can convince anybody...
T*sin(climb angle) - D*sin(climb angle) pretty well cancel out, and are an order of magnitude smaller than L and W.
ft,
Stick with the original coordinate system.
Otherwise your "L = W*cos(climb angle)" is wrong for a steady-state climb condition.
If you convert to a coordinate system locked to the velocity vector, the weight of the aircraft is no longer W, but W / cos(climb angle).
CJ
PS: VTOL is not really relevant here, no?
No lift, no drag. Just T=W.