The supplies at short-circuit.com all look like they put out way too many amps: even the 100W fanless brick says it puts out 10A. If I recall correctly, the Pico 150 is only rated for 8.5A input. That would start to fry stuff, wouldn't it?
No. The current is not "put out" by the power supplies in the sense you are thinking. It is drawn
by the circuits and devices that we connect to the terminals of the power supply. The rating of 10A only says that it is the maximum
current that can be drawn from the power supply. If you draw less than that, the power supply will be quite ok with it. Your PC will draw current from the PicoPSU which will in turn draw current from the powerbrick. So it is perfectly fine to use a powerbrick that has higher wattage than the PicoPSU.
The main difficulty we are worried about in mating the powerbricks and the Pico supplies is the connector
that is used to mate them. This is somewhat like the tail wagging the dog! The 2.5mm jack and the Molex pins can handle somewhere around 6-8A of current. If you draw more current through them, they will overheat and might scorch whatever is in their vicinity. So, the Pico 150's manual says that, if the input current is expected to exceed 8A, then you should use a 2x2 Mini-fit Jr connector instead of the 2.5mm jack. Once you do that, the current gets split two-way, and each pair of pins will handle half the current. The only reason this is more complicated than hooking up a standard connector from Radioshack is that the Mni-fit Jr connectors are typically sold to OEM's and, so, the information about them is not tailored to end users. But, hopefully, the information I have documented on the other thread is helpful in doing this.
Some soldering will be definitely involved. If you want to put a connector at the end of a wire, soldering is a common method. But if we are trying to put a 2x2 connector, then we have to split a pair of wires into two streams and connect them back at the other end. Soldering is even more crucial for these junctions. I haven't found any way to avoid this soldering.
Electrodacus's set-up doesn't have this problem because his design uses a 4 pin DIN connector to start with. So, no end-user tinkering is involved.