βSimp=Factor; SetAttributes[βCollect, Listable];
βCollect[B[ω_, Λ_]] := B[βSimp[ω],
Collect[Λ, (Subscript[h, _]), Collect[#,(Subscript[t, _]), βSimp]&]];
βForm[B[ω_, Λ_]] := Module[{ts, hs, M},
ts = Union[Cases[B[ω, Λ], (Subscript[(t|T), s_]) :> s, Infinity]];
hs = Union[Cases[B[ω, Λ], (Subscript[h, s_]) :> s, Infinity]];
M = Outer[βSimp[Coefficient[Λ, (Subscript[h, #1]) (Subscript[t, #2])]]&, hs, ts];
PrependTo[M, (Subscript[t, #])& /@ ts];
M = Prepend[Transpose[M], Prepend[(Subscript[h, #])& /@ hs, ω]];
MatrixForm[M]];
βForm[else_] := else /. β_B :> βForm[β];
Format[β_B, StandardForm] := βForm[β];