For the constant-on tunnel illumination with 32 (or whatever many) LEDs, I recommend a DC-DC converter module. Otherwise, as discussed above, when starting from a "high" voltage like 18 V and dropping (via resistor) down to 3V, most of your power is going up as heat in the resistor. A DC-DC converter module uses switching circuits to more efficiently convert the power from one voltage to another so you don't waste power as much power.
Search eBay for "LM2596 module" and you'll see these for 99 cents and that includes shipping! It's an extremely good value. You can buy versions that have a bridge rectifier already installed on-board ("LM2596 AC module") but they are more expensive considering you can buy a bridge rectifier for $1 or so on eBay (any bridge rated for at least, say, 2 Amps and 100V).
So you apply AC from your CW and adjust the module to put out some lower voltage like, say, 3.5V to drive a parallel string of 32 or however many LEDs. In this case the resistor will be a much smaller value so the power it wastes as heat will be much smaller. If you have an unused 9V, 12V or whatever wall-adapter with DC output, you can skip the bridge rectifier as you already have DC. You will need a voltmeter to adjust the output voltage but as I was advising a guy in another thread you don't need a fancy meter and Harbor Freight Tool stores if you have them in your area give these away free (with coupon) shown here being used to adjust the module output to 3.0V which is what he wanted to drive a string of a parallel LEDs.
Speaking of parallel LEDs, this reminds me of another freebie I picked up at Harbor Freight - a small 4.5V operated LED worklight that has 24 parallel LEDs.
All those white LEDs are wired up in parallel just as you're planning to do...and note they use a 1.5 ohm resistor. But this is, in part, because they are starting from about 4.5V (3 1.5V batteries). If you choose to use a DC-DC module where you can precisely set the output voltage (the voltage output is regulated so you set-it-and-forget-it), you really don't need a resistor at all if you are driving all like LEDs.
