Electricity kills you in basically two ways. First of all, it can interrupt your heart’s normal way of doing things. Once you get your heartbeat screwed up, it doesn’t tend to fix itself, and eventually you die from lack of blood flow. However, this isn’t how an electric chair kills you. An electric chair uses the second method, where basically it cooks you to death. The theory is that there’s enough damage done to your brain in the first jolt that you don’t feel the rest, otherwise it would be a fairly gruesome way to die (which is the stuff for a different forum, or at least a different thread).
Directly relevant to this thread, what you need to do is basically increase the cooking power of your chair. The first thing you would want to do is make sure that your chair has good connections everywhere. A bad connection won’t allow as much current to pass through it. A bad connection will result from things like corroded copper in one of the wires or connections, or a dried out or synthetic sponge where the connection to the body is made. A wire that is too thin would also count as a bad connection, since it will lose all of the power in heating up the wire and not enough current will get transferred to the victim. All of this is number 2 on your list, increasing the current, but we’re not changing the voltage yet.
The next thing to do would be to change the voltage (number 1 on your list). If we increase the voltage, all other things being equal, the current will also increase.
Note here that we’re kinda focusing on the current delivered into the load, so that’s why electricians have the saying “its the volts that jolts but the mills that kills” (meaning milliamps, or current). But really it’s the power transferred to the load that matters (power is voltage multiplied by current, for those of you that slept through your circuits classes 
). By focusing on the current delivered to the load, you focus on the actual power being delivered, not the power lost through bad connections, thin wire, etc.
We’re kinda focusing on an electric chair here, but the principle is the same for other things as well. There are many things besides the source voltage that determine how much current actually flows. It’s not the source voltage that gets you. It’s how much actual current you get to flow, which translates into how much power is actually delivered to the load, that causes the real damage.