The tone you seek is about cranking a tube amp until you get that natural compression related to that Knopfler tone signature. Its known that in this particular Era, he uses Soldano SLO amps apart from others; it’s hard to tell precisely.
But the good news is that you can probably nail the tone with some pedals and your current rig.
MK often uses compression on lower watter amps and some overdrive as boost pairing with an analog delay for that final texture instead of reverb.
To get that characteristic eq curve, I would suggest a tube creamer style pedal with mids control, one good classic-like compressor and one analog delay.
For the TS, maybe the Maxon ST9pro+ is the right choice because you can set it with low gain to boost and slightly drive, and you have the extra features of low boost and the mids knob that will help you tweak the tone for a warmer setting.
My choice for the compressor is the JHS Pulp ‘n Peel because it’s based on the orange squeeze that MK uses in some songs and will help you get that natural compression and sustain with the Epiphone amp.
And finally, don’t use reverb but use an analog delay to give that final tone texture with no modulation and low regen and mix settings.
Your guitar is not ideal because MK often uses positions 2 and 4 in his strats, so you must carefully dial the eq in the amp and pedals to compensate for that. Maybe modding your guitar for coil-split will help too.
Let me know the ones you will get
and maybe share with us some sound samples then!!!