What was the logic of combining lift engines and variable geometry wings? Was this just a combination of the design fads of the era? Or was there some logic to it? To me it seems like two fundamentally opposed approaches to the same requirement.
Variable geometry is an aerodynamic approach. It lets you combine a wide-span, high-lift wing for STOL operations with a highly swept wing for low gust response at low levels and high speeds. The wing is complex and heavy, but the power-plant arrangements are fairly simple and the required thrust is modest.
Lift engines rely on thrust to achieve what the VG design does with aerodynamics. Lift engines allow VTOL, so you can dispense with the large wing altogether and have a stiff, light, short-span unit. But the power-plant arrangment is heavy and complex, and you need more thrust to get off the ground than you can use in flight.
Combining the two approaches thus appears to make no sense (except on the contractor's bottom line, no doubt). If you choose the STOL solution, you do not need the extra weight penalty and complexity of VTOL. If you choose VTOL, you do not need the extra weight penatly and complexity of STOL.