Has all routine maintenance been performed to the car, to include:
60k timing belt, OEM tensioner, balance shaft belt and pulleys
ECU removed and inspected because if this ECU uses the same capacitors the 1989 Mitsubishi products (+ onward) that came to these shores, they are over due for replacement and will be leaking.
Granted you may have a dual board setup in your car (unsure when the split was by memory) but most ECU's up into the 1995+ range, were affected by this.
$2 in parts or a wasted ECU due to damage if left unchecked and acid eating into traces or blowing parts due to shorts/over heating.
There is an ECU rebuilder in the US known as ECMLink (yes, the upgrade chipset and software makers) and they repair ECU's like these for turbo cars, so if you have any issues with yours please post here and we can direct you.
Okay, those are the basics.
I will say that the FPR in factory form is probably designed to keep fuel pressure in the rail for some time, as is a higher pressure when hot restarting on USDM cars that have a FPR solenoid to block vacuum on hot restart - the solenoid may or may not be on your car due to likely more lax emissions on cars in AUS/NZ during that time period - you guys had carby cars well into the 1990's IIRC!
If the FPR is worn out, this could have an effect on cranking time,
If the check ball in the OEM fuel pump is no longer seating properly, that can allow bleed back to the tank, either rapidly or over time.
I can never remember each individual setup with regards to pump and or FPR having a check system, but either could be an issue.
My modified and likely somewhat tired motor takes 4-5 seconds of cranking to get started, from cold and no difference to that timeline with ECMLink triggering the moment I am key forward before cranking, to prime the fuel pump for a 10 second window to assist fuel pressure at start.
Get the engine warm and the engine fires very quickly, because compression is up due to everything having expanded to operating size and function. Old motors that are modified make cold starting that much harder due to lower compression, cam overlap, worn rings, etc.
These would be the things that stick out in my mind.
Stock copper factory plugs, is where I would start, along with any belt maintenance, because if either timing belt snaps, the motor is coming apart.
After plugs, if nothing changes ... I would head towards fuel assuming your spark is strong and tested.
Fuel pumps should be easy to get a hold of and there were drain plugs on certain fuel tanks made early by Mitsubishi - thank them for that!
FPR fuel pressure regulators like OEM may be more troublesome to acquire but I will give you a couple sites to build your car with, and should give you an idea of parts are available and to compare prices against, UAE and Japanese warehouses OEM.
<- based in the UAE, parts middle men with a great catalog
<- based in Singapore, parts middle men, good chance based on percentage availability of finding parts on a shelf in Japan or UAE, truck or car warehouses because parts were used in both
Great way to cross reference between the two sites and then go worldwide via google or similar search engine.
Keep in mind, your motor could just be getting tired.
Compression check cold, dry, plugs removed - throttle wide open, 5x full engine revolutions or until max PSI in the pressure capture gauge is shown
Compression check cold, couple drops of oil down a lower reading cylinder, ^ same procedure as above
Compression check hot, one cylinder, dry, plugs removed ^ same procedure as above
If cold readings are pretty close to one another, that is great news, even if they are read a little low. One low cylinder can indicate valves seat(s) bad and or ring sealing now weak.
If oil added reading jumps way up and otherwise cylinders cold were close to one another, you have tired piston rings.
The FSM manuals are on here, check the News from Admins section, as compression checking pressure should be listed for 1.6 NA, 1.6 turbo and smaller 1.5L motors. 89-92 CSM or 89 Colt Mirage turbo folder.
I just went through an ordeal with my car starting poorly once warmed up or simply restart even cold, but could otherwise drive properly for 1hr plus. Ignition transistor replaced and for good measure my ignition coils and tachometer interface, issue solved, plagued me for
likely 10+ years, but I had driven the car so little between repairs and restoration. I would not be leaning towards that being your issue, but anything is possible as electronics age.