You would need three round timers for the normal rounds (they can get reused each round). The first would be the neutral timer that would stalemate if it ran out before either team was able to capture the point. Then you would switch between the other two timers depending on which team held the capture point.
Likewise you would also need extra capture point entites (the parts with the spinning holograms). You need one capture point for each spawning area. These can be hidden. Then you need one capture point for each in-between area, which are what you'll actually use for the KotH mechanics. Once a timer runs down and a team wins, the spawn-area CP of the other team will get triggered to switch owners.
The layout would probably look something like this:
A, B, C, and D are hidden points that correspond to spawn rooms. AtoB, AtoC, AtoD, BtoC, BtoD, and CtoD are your KotH points in the middle of the between areas. BLUE and RED are the capture points for the final rounds (presumably you'd keep them attack/defend, to prevent stalemates, but KotH final rounds are possible).
Possible things that might go wrong:
a) This would require eleven cap points minimum (twelve if you have separate rounds for AtoD and BtoC, which is the usual way to do it), but I've heard that there's a limit of something like eight that the game can handle before bugging out. One can hope that if you're only dealing with three at a time, it might not be so bad.
b) I haven't tested this empirically, but I believe it chooses the next round based on priority and whether or not the team owns all points listed under "Control points in this round" in the round entity properties. Normally you would just have it as "A B" or "B D" depending on the round. However, with the third KotH point in the middle, you'd need to have it listed as "A AtoB B" or "B BtoD D" in order for your point to actually show up in the HUD. This means it's likely that the game will force you to play all six combinations in the middle before letting you play the last round. One way around would be to have some complicated condition checking, and if you own B and capture C, it will automatically give you BtoC, assuming that was not the round you just played to win C.