I have an Olympus BHM as well, just need some time to get it going. Unfortunately the light source was broken on it like yours. Thanks for that info on the LED upgrade, will read in detail.
For my next microscope illuminator project, I've come up with a better way of constructing the optical concentrator. Two parts combined:
* Ebay search term: LED reflector collimator eg item 371258089004 and many others.
There are sizes to suit the 10W and 50W flat LEDs. You may find that alone will work well enough with the lens included. Beware that what you end up with is a nice focused image of the LED chips.
I'll be using just the reflector part, to get better matching from the LED to the concentrator cavity, and allow homogenizing of the light.
* I'm planning to use several large LEDs combined for colour control in this one. So still need the optical concentrator method. But I'll be trying making a solid former of the optical cavity shape first (probably of wood), then molding the body structure around it. Either in casting epoxy or wrapped and soldered copper sheet.
Then gluing reflective foil to the inside of the cavities, same as before.
That project is getting posted here as it progresses:
http://everist.org/NobLog/20150628_LED_lighting_mk3.htmThe 10W colour LEDs arrived today.