Thanks for the advice!
I'm still learning how to use my oscilloscope, but here's a screenshot of what I'm seeing currently. I should note that this is with my probe set to 10x, so the peak to peak is actually 10x worse than than what's being displayed under the measurements, right?
That's with the output set to zero or so? Yeah, doesn't look good.
Your scope+probe probably don't automatically switch when you switch the 1x/10x switch so you'll need to do the math in your head or set the scale factor for that channel in a menu (if possible). So, yes, the voltages are 10x bigger than implied by what you see.
I have one of these (a 30 V, 2 A model) in similar condition, but mine works up to ~ 1/2 rated voltage, then begins to oscillate. So the bar graph looks fine from 0-15 V, then turns into a blurred full-scale mess above that. My plan (if I ever get around to it) is to re-cap first, then hunt down remaining problems, if any. I already replaced one big filter cap after finding it had nearly no capacitance and high ESR.
If you don't already have one, get one of those cheap component testers as discussed in
this thread. They will measure capacitance and ESR for capacitors, and will identify, test, and measure almost any two or three pin device (resistor, capacitor, inductor, diode, zener, NPN, PNP, JFET, MOSFET, Triac, SCR, etc. etc.).