Suzuki m13a has no carb. Efi.
Faulty map will misread air coming in and fuel/air ratio would be out
Back firing = unignited fuel being ignited in the hot exhaust/manifold backfires can happen in the intake too so . In this case more throttle = louder backfire. Definitely no lack of fuel.
A compression test will let you know if cam timing is good. Good compression = good timing (for now). Vehicle at operating temp and cranked with WOT will give correct results.
It runs well when cold and only gives problems under load when warm but not problems sitting at idle all day when warm, correct?
Japanese Escudo, '93, 4 door, 16v, 4 spd Auto trans, 4WD, Auto locking hubs