...I found these and ordered them to tinker with.
They are AC DC converters .5A 6W LED Driver Transformer for $1 each.
AC in 12V DC out.
What might these accomplish in lieu of the simple diode approach?
Worth the dollar?
That module is NOT in itself 12V DC out. As Chuck says, you will need additional circuitry to limit the current flowing into your LED strips. That is, with your 14V AC input, that module will put out about 18V DC which will overdrive the nominal 12V DC LED strips.
There are 2 things going on here. 1) convert AC to DC since LEDs operate on DC. 2) adjust or regulate the DC applied to the LEDs to within their operating range.
It's coincidence or just dumb-luck that using a single 1N4001 diode with the 14V AC Accessory output of a train transformer does not require step 2. Chuck did the math earlier. By using the 4-diode method (full-wave instead of half-wave) in conjunction with the capacitor (the big black component on the module), the math gets messier but bottom line is you now need step 2.
Step 2 can be as simple as a 5 cent resistor which provides a fixed brightness; some math is required to choose an appropriate value based on how many LEDs you're driving. Most guys will pony up $1 on eBay (free shipping from Asia) to get a DC-in, DC-out converter module which provides adjustability. Two examples (photos hijacked from another thread):
You would need a meter to set the voltage to between, say, 10-12V depending on brightness you want. For about $2 you can even get a DC-DC converter with a built-in LED digital voltmeter! You can get DC-DC modules that have screw-terminal in-and-out rather than having to solder wires. And so on.
Apparently you already purchased the AC-to-DC module, but for under $3 you can get a single module which performs both AC-to-DC conversion and output adjustability.
Note that above module even has mounting holes; I noticed in your earlier photo that you neatly mount your components using screws.