The kit states "13.8 V" on its schematic (the "standard" amateur radio voltage), so I'll use about that voltage for testing.
The power supplies I own are a bit limited. My HP E3631A is adjustable, but can only put out 1 A.
I have a fixed 13.2 V (so not quite 13.8 V) power supply that can deliver 3.5 A continuously / 4.5 A intermittently. It's what I've used so far.
During the tests, I managed to pull about 6 A pretty early on, so a new power supply is needed. I ordered a new one from AliExpress called "PS30SWVI" (Power Supply, 30 A, Switching, sixth generation). It even have double Anderson powerpoles on the front! It should arrive in about 2 weeks from now...
With the new power supply I should be able to adjust the voltage and have plenty of current available. My only worry is that it doesn't have any settable current limit, but I guess that I could ad a fuse in series.