Why won't this charge pump supply more than a couple of milliamps?
2mA sounds about right.

The datasheet of the SN74HC14 says it has an output current of about 4mA.

You are doubling the voltage.  That means twice as much current must go in on the low side as you take out on the high side.

4mA available on the input gets you 2mA available at the output.

You need to supply more current going in.



I don't think a simple transistor will do it - you need to drive the charge pump high and low.

You need something like a "totem pole" output stage.

Here's an example from the wikipedia article on TTL circuits:



You need the stuff around V2, V3, and V4.  It could also be done using a PNP and an NPN transistor.  You only need two transistors instead of three, then.