I remade another soldered circuit, adding extra 100uF electrolytic bypass capacitors at the input and output of the voltage regulator and ensuring that every grounded component now has its own path to ground rather than going through other elements. This circuit now seems to be working just like the solderless circuit. Attached is the transfer function of the soldered circuit, which matches with the result from the solderless circuit.
Here are both on the same figure- they are about overlapping but are slightly different if you zoom in enough.
I have also attached a new version of the circuit schematic to reflect the changes and to make the physical layout more clear.
My next step for these last few days this summer will be designing a PCB using Altium. I've emailed Varun about how to use Altium on the iMac but he hasn't responded. If anyone else knows how to use the software, please let me know.