First thing first, rather than Tezgam, we've been taking Karakorum Express (last June 2018) Karachi-Faisalabad, 16hrs, then Faisalabad-Rawalpindi New Subhan Skyways (Daewoo type) right outside the station and ready, 4 hours.
In total it takes 20-21 hours, saving ~6 hours and related cost, mostly because Tezgam has to go Lahore which is a detour