So, I ordered a quart of resin April 18, and it arrived April 27th.
Today, I got around to shooting it with an Edipower 10W 405 nm LED. The LED was driven with a current limited lab power supply at 1.04A and just over 10 Volts. I'd previously bought the LED off eBay, and can't seem to find the original datasheet for it. At the time, I was interested in using it to expose dry film photoresist for PCB artwork. It actually works quite well for that exposing a 6" square area in perhaps a couple minutes through a piece of white copy paper. If memory serves correctly, it puts out somewhere around 1W at 405nm into a 120 degree beam. The LED is 9 emitters, 3 parallel strings of 3 in series, spread out over less than 1 cm^2.
This LED isn't a toy like the little keychain lights for checking for counterfit bills. From 10 feet away, you can see glow from fluorescent labels, and a bit of glow from other things. It is moderately hazardous, and although borderline UV, the usual hazards of UVA and deep blue lasers apply, such as increased risk of cataracts. You can feel a perceptable wamth on the back of your hand. Think about what it can do to your eyes if used carelessly. We'll definitely want a gaurd like a piece of orange or red fluorescent plastic to view the work and a safety switch connected. That isn't as bad as it sounds, as you don't want to expose the unused resin anyway.
A four minute exposure at 5cm distance produced a slighly tacky, but stable suface (tacky but incompletely exposed after about 2 minutes) on a white business card. The deposit was 0.035" (almost 1mm) thick.
This equates to an exposure of about 100 mJ/cm^2 for a 1mm thickness without the benefits or losss of any optics.
While there are shorter wavelength LEDs, and the polymers are likely more senstive, they are also less efficient electric to optical. This is an older LED and it might be possible to find a 385nm emitter with about the same optical efficiency. If the chemistry is at all similar to the dry film resist, they might be twice as sensitive.
The bottom line is an LED source is probaly viable with a DLP projector engine. If not this one, higher power ones are available.