Regarding PEK: It is doable while a massive gamble. Done that before (on separate tickets too), but you would need a flexible ticket. But agree that this is not a viable back-to-back destination.
Things you need: A flex ticket so you can change you flights before departing HKG, the boarding pass for the return leg (paper ones).
Make sure you are booked on the same aircraft (risky coz they could change the aircraft at PEK)
On KA the turnaround time is usually around 1:10-1:20, if the aircraft parked at a gate far away from the transit checkpoint you WILL need to walk fast. Prepare for an awkward conversation with the securities but they should let you through.
Unless you are desperately unlucky, you should able to make it back to the gate before they even start boarding.
If there is an ATC delay from HKG, forget about it, change your tickets to another day before you board the flight to PEK.
Don't even attempt it if you are not on a flex ticket.
Also, TPE should probably be excellent if going through airside. Good transit facility (usually empty).