[Mondial]

That first IF transformer is indeed unusual, but it might be explained by the fact that it is driven by a triode mixer. In the usual case of a pentode or pentagrid converter, the impedance level seen by the transformer primary is on the order of 500K ohms or so. A triode however has much lower plate resistance, typically around 10K, so the primary sees this lower effective impedance and must be designed to match. This might explain the much lower DC resistance and the need for permeability tuning to permit the use of a larger value resonating cap than normally available as a trimmer.

I would guess that a higher value cap is necessary than usual to tune the primary to resonance. You could experiment with various values of capacitance until you obtain a sharp resonance peak at the center of the tuning slug range.

Did the cap you removed have any marking as to its value?