When making the power supply, start by running the probe directly on a variable supply and slowly raise the voltage until the current draw stops changing (while touching the probe tip to give it something to amplify). Design the supply for that voltage. They use a 5v regulator on the probe board and that will need more than 5v to work properly. Feeding it a higher voltage than necessary will make the probe heat up faster. It will be around 6v.
Edit: I honestly cant see what regulator they used. Maybe they used a 3.3v or something else, but I doubt it. You'll find out when running up the voltage.
I added a buffer amp to mine and made the mistake of feeding it off the unregulated side, so where the buffer is biased right is not where the current levels off. I plan to rebuild mine, fix that mistake, and add the demodulated output feature yours has.