Best route of all is Islamabad Airport to Karachi Airport however based on my experience here is a guideline,
2 nights stay
Isl to lhr via motorway night stay at lhr (4-5 hrs drive must be during day time to avoid fog) excellent road
lhr to mirpurmathelo night stay at mirpurmathelo (approx. 10-11 hrs drive via Sahiwal bypass route) good road condition but traffic which can at time restrict your speed to even 50km/hr
Mirpurmathelo to kci (approx. 10 hrs drive) good road condition but again a lot of heavy traffic
1 night stay
isl to rahimyar khan via faislabad bypass, gojra, multan, bahalpur (12-14 hrs drive depending upon ur speed n stops) good road condition however shorkot patch of almost 50 km or so in pathetic condition and also multan bwp bypass not good while travelling back from kci to isl)
rahimyar khan to kci (12-14 hrs drive) road condition same as explained above.
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.Still my advise to avoid travelling by road