It seems the reality of the filter, whilst quite sharp, is NOT centered on the desired 136 to 137khz. Whilst I appreciate you saying this is not an ideal filter design, it's what I have on a stripboard (and you'll possibly condemn the use of miniature leaded inductors, I don't know... ).
Ew, mini inductors... those don't have very good Q's.
Consider, you set out to design a filter for -- well, hmm, you didn't really give a spec, you did say 136-138kHz inclusive, but it's not clear how tight around that you actually wanted.
Your filter sim shows about 7.6kHz BW, which implies a filter Q of 18. Commodity coils will get close, but not really be safely above; they certainly won't be the 200 specified in the simulation! You'd have to shop around to find better ones.
But if you're happy with a Q even lower than this, and don't mind a few dB more insertion loss, commodity parts will do well enough.
It's not a matter of me condemning something. That implies I care about some sort of judgement. I don't. It's your radio, it's all up to you if it's good enough or not.
All I can tell you is whether some component is likely to meet your need.
But it is what is for now, how might I shift the passband a bit lower, using readily available caps or standard leaded inductor values please? I don't think an trimmer cap anywhere in the circuit is practical, is it?
Yeah, trimmers don't really come this large. Easy hack: put capacitors in parallel with what's already in the circuit, to increase their values incrementally. Tedious (lots of poking parts in and out), but it is what it is.
Incidentally, it's tempting to hold a capacitor in your fingers (or pliers or whatever), and poke the leads at the circuit. But be careful here, because your fingers have lots of capacitance and resistance. You can probably get away with this on the shunt branches (i.e., in parallel with your stage 3 / Jay's C2), because the impedance is low there. You probably won't get away with it on the series branches, which are high impedance, very sensitive to stray capacitance and resistance.
Easy enough to test -- touch one end of an inductor and watch the passband go off in the weeds!
Lots to learn, especially that a modelled circuit may not be the same when built
As I have said many times before and will likely continue saying forever -- it is a poor modeler who blames his tools. There is no bad model, only an incomplete model!
In this case, you've probably not modeled the input and output impedances correctly, and haven't specified the component values and losses accurately. (As Jay notes above, tolerances are important for a filter this tight -- something you cannot possibly get from commodity (typically 5% or worse) parts!)
Tim