Electronic – Switching power supply only works when warm

Is there any danger in bonding the DC- output to Ground with a short wire, to ensure my circuit ground is also referencing the home ground? I'm not sure simply letting the outputs float is wise,

Assuming the power supply is properly built either is fine.

Side-note: I have an after-market laptop supply that's two-prong... it works either way, but if I plug it in one way the metal trim on the laptop has an interesting "buzz" to the touch. Not shocking, but definitely noticeable. I suspect that when it's plugged in the right way the output ground is weakly referencing neutral, and the "buzzy" way has the output ground weakly referencing line voltage (it's floating - it'd be quite a bit more than buzzy otherwise). The OEM supply with the 3-prong plug? Fully grounded to the shield of the DC power cord.

Power supplies without an earth connection often have problems like this, especially as they get larger.

Capacitors have to be placed between input and output to control EMI. In an unearthed design this ends up with the output being "weakly referenced" to the input. How weak that reference is (or to put it another way how big the "touch current" is) depends on the size of the capacitors. Unfortunately there is a tricky compromise here, bigger caps are better at suppressing EMI but produce larger "touch currents". Larger power supplies tend to suffer worse from this than smaller ones (this is why laptop PSUs from reputable brands are usually earthed while phone chargers are usually not).

In an earthed design this can be mitigated either by tying the output to ground (pretty much universal in in desktop PC power supplies, occasionally seen in laptop supplies) or by splitting the EMI suppression capacitors into two parts, one from output to earth and one from input to earth.

After repairing a returned unit, take a very careful oscillogram across the Schottky with a short 10:1 scope probe (directly connect the tip and use a very short ground wire) and no bandwidth limiting on your good quality (100MHz or better, digital storage preferred) scope.

An example of a short probe, borrowed from elsewhere on EE.SE:

What you're looking for is high voltage (a spike, or ringing) on the leading edge of the voltage waveform. Any time you switch an inductive load, there's the potential for high voltage - unless you carefully look for it (i.e. with a short probe and a good scope) you won't see it. Your layout will have a great influence on whether or not there will be nastyness across the Schottky, so measure to be sure.

If you do end up seeing something ugly, you may need to introduce an RC snubber across the Schottky to keep the diode from avalanching.