Considerations specific to kings/kingdoms as vassals
A kingdom with an active title will not de jure drift into your empire unless the kingdom's de jure empire title exists. (May have changed in patch 1.10)
Kingdoms have their own crown laws (crown authority, investiture), even when part of an empire (I am not completely positive, especially with patch 1.10, but that is what I have observed)
You cannot press de jure kingdom claims for your king vassals. The king can press his own de jure claims. You can press de jure ducal claims for your vassals, but not your vassals vassals.
Prestige. For a big enough kingdom (enough duchies) you would get more prestige from duke vassals than a king vassal.
Considerations similar to duke vassals, but amplified
Kings will want all territory in their de jure kingdom which will be bigger than a duchy.
With better marriage prospects, kings may obtain more powerful allies.
The increased power of kings makes them more capable to
- Rebel
- Conquer foreign territory
- Conquer other vassals in your kingdom
When the crown authority prevents you from waging wars with other vassals, there are a few things you can do:
Start a Plot to force your liege to lower crown authority.
You can invite other vassals of your liege to join your plot, although this will depend greatly on how much they like you and how much they like your liege. I often try to grease the wheels by giving them gifts or fulfilling wishes ("wants to marry"). You also could have your chancellor sow distrust, although in my experience that does not succeed often.
Careful manipulation of marriage and murder.
This is normally best done with young adults who are over 16. Find a Duke or Count that has one son (his heir) and a daughter. Arrange a marriage between YOUR heir and THEIR daughter. Once the marriage is nice and locked in, see if you can't knock the only son out of the picture with a well placed assassination plot. It will also be helpful if the target Duke or Count is older in years along with his wife. Keep an eye on his wife from time to time to make sure she is not pregnant.
Have patience.
Sometimes the easiest thing to do is just wait for the current leader to die and the realm to fall into anarchy. Civil war will often break out after an Emperor dies, especially if the heir to the throne is young or if there are many claimants in the family. You can take advantage of the chaos and claim independence, using mercenaries to strike quick blows to force the new liege to yield. This is risky, however, due to the possibility of the Emperor regaining control and bringing about a stable rein. Generally, the more chaos and unhappiness there is within the Empire, the easier it will be to tear pieces away.
Just a few ideas. There are always more ways to get from A to B. I enjoy the challenge of claiming territory within a larger Empire, but you do get a bit stuck when crown laws get to high. In my experience, however, the more they tighten their grip, the more vassals get revolt-happy.
Best Answer
Leave him imprisoned. He's far more useful to you that way.
Keeping him imprisoned will mean the HRE will be a regency. Regencies have a lot of restrictions on what they can do, which is perfect if you want to become more powerful.
Regencies are also vulnerable to factions. Regents typically fold to faction demands more easily and will automatically accept any faction if they are in it. Either become the regent or get him involved in your crown authority faction and you'll be able to lower it all you want.
Having the enemy leader imprisoned also means you automatically win any wars against them. If you want a quick and dirty method to drop crown authority, start a faction and press it. You are now at war with your liege, with 100% warscore, so you can enforce demands right away. This will release him though so it'll only work once.
Of course, this isn't limited to Lower Crown Authority wars. If you were to make a faction about something else, for example, making someone else emperor, that'd work too. And since anyone eligible to vote is eligible to take the title this way...