i have been struggling for years with orchids...my home depot setup is an array of 6-8 simple reflectors with ge daylight cfls... i put parachute fabric over them - use 2 silver/ gold reflectors and a few makeup mirrors to try to get the color/light for what i am looking for...
It's hard for me to offer anything definitive because I don't know the details of your lighting/camera color filter array, but I can give you a few things to think about. The first has been mentioned already: IR-cut filters. The second has not received any explicit attention in this thread: the smoothness of the spectra of your lights. Compact fluorescent lamps usually offer emission spectra that are quite peaky. There are versions that moderate these tendencies; they usually advertise a high Color Rendering Index
(CRI). I would advise trying some CFL's with CRIs of around 100. There's no guarantee that they will work better for you than what you've got now, but it could be a cheap experiment compared to buying new strobes.
There are several reasons why a CRI of about 100 is not a dispositive condition for better color rendering in photography. The first is that the CRI is predicated on the human cone color sensitivities, not the sensitivities of the filters in your particular camera. The second is, as the Wikipedia article referenced above states, the CRI is not a perfect index of the effect it is trying to measure. Still, A CRI around 100 tends to mean a smooth spectrum, and a smooth spectrum light source tends to be better for avoiding unexpected color shifts. I would avoid sources with CRIs much above 100, because they may use tricks to emphasize portions of the spectrum to fool the eye into thinking colors are richer than they otherwise might be perceived, and those tricks might not work on your color filter array, and might nt produce results you like even if they did.
You say you are using colored reflectors to modify the light. If the source has a bunch of narrow spectral peaks, the reflected source will (usually) have them too, but the relative amplitude will be affected. Therefore, you can't filter a peaky light source into one with a smooth spectrum.
In general, it would be a good thing for you to look at the spectra, or at least the CRI, of any light source you're considering. (strobe, HID, LED, etc). An incandescent source will naturally have a high CRI if there are no tricks employed in the design, but they tend to run to warm color (photographically warm, which, confusingly, means a cooler color temperature), which may not be what you want for orchids. They're also hot, which is almost certainly not what you want for orchids.
LEDs are not usually stellar CRI performers, but they are a thermally cool source, and are readily available with color temperatures of 5000 degrees Kelvin and higher. There is a series of LED bulbs produced by Cree that, while not intended for photography, have CRIs in the mid 90s. Here's one
, but it's 2700 deg K.
Hope some of that helps.