FIRST OFF: USE AT YOUR OWN RISK! This hack involves modifying a 120volt LED bulb. I can't be held responsible if you electrocute yourself, burn down the house, or create a temporal anomaly. You have been warned.
However this is pretty straight forward, doesn't involve messing with the internal wiring of the LED bulb, and there are only low voltages on the LED side of the unit.
My over-the-stove microwave has an appliance bulb (I usually install a 40W T8 Intermidiate Base). No one makes an LED replacement. Meanwhile because most people tend to slam the microwave door, that bulb lasts MAYBE 3 weeks.
I also have LED lights under all my counters, so I'd like to have a matching WHITE LED light under the microwave instead of the orange incandescent.
I've been all over appliance forums looking for a solution, and people are reporting that they have just had to hack their own bulbs, which is what I did:
FIRST you need an intermediate base to candelabra socket reducer because no one makes an intermediate base LED, but there's lots of candelabra base LED bulbs.. I bought this reducer from Amazon:
http://www.amazon.com/gp/product/B0067B ... UTF8&psc=1

Then I looked around for a candelabra base LED with the shortest base containing the electronics (all candelabra bulbs are too tall but they can modified since most of the bulb is empty space and a plastic reflector). I found this 40w bulb at Lowes:
http://www.lowes.com/pd_394796-75774-LC ... d=50109728

The bulb I bought was clear not frosted, but it's the same model, and it doesn't matter.
Then I snapped off the clear plastic "bulb" which is just glued on and easily came off.
Then I removed the plastic reflector lens which was attached with two jewelers size Phillips screws.
What you're left with is an LED bulb that is just slightly longer than the original T8 bulb (you'll want to put the screws for the reflector back in otherwise the base will come apart - in the photo below I haven't put the screws back).

Even though all the light is shooting out the top flat end, there's more than enough light reflected around inside the bulb compartment of the microwave to provide plenty of light.
EDIT: I also placed a small sheet of aluminum foil above the bulb to help reflect more light down.
The only question is how it will hold up in the long run. The LED does get hot, and they warn you not to mount it in an enclosed area. However the bulb compartment is not enclosed - it's actually open and probably shares airflow with the vent.
EDIT: Still working fine 2 weeks later.
The only downside is the bulb (despite being dimmable) does not noticeably change brightness between the two brightness settings on the microwave (low & high). But that's fine with me.
Here's what it looks like - you can see how the light level and color nicely match the under-counter lighting:

