How do you program a completely transparent crossover?
I'm no expert but I'll explain how I would approach this. In general, crossover design involves selecting your respective cutoff frequency (or frequencies, in your case) and desired attenuation or filter order, and deciding on a filter type. Trivially, a Butterworth filter is a popular choice as they are easy to design and implement. According to Wikipedia, a better choice may be the Linkwitz-Riley filter:


  A Linkwitz–Riley (L-R) filter is an infinite impulse response filter used in Linkwitz–Riley audio crossovers...It is also known as a Butterworth squared filter. A Linkwitz-Riley "L-R" crossover consists of a parallel combination of a low-pass and a high-pass L-R filter. The filters are usually designed by cascading two Butterworth filters, each of which has −3 dB gain at the cut-off frequency. The resulting Linkwitz–Riley filter has a −6 dB gain at the cutoff frequency. This means that summing the low-pass and high-pass outputs, the gain at the crossover frequency will be 0 dB, so the crossover behaves like an all-pass filter, having a flat amplitude response with a smoothly changing phase response. This is the biggest advantage of L-R crossovers compared to Butterworth crossovers, whose summed output has a +3 dB peak around the crossover frequency.


Wikipedia on L-R Filters

I would design these such that the bands of interest are all separated out nicely, either through some sort of series configuration or by explicitly designing bandpass filters instead of lowpass/highpass filters (except for your lowest and highest bands of interest, of course).

This could either be done by designing the filters as analog and then using a bilinear transform to bring them into the Z-domain, resulting in a form that could be implemented in your language of choice, OR could be done digitally from the get-go in Matlab or Python (using SciPy's iirdesign() function).

SciPy's IIR Design Function

Then, you would need to implement them in whatever language/platform you're using (although I would hazard a guess that its C++ on Windows/Macfor a VST?).

Additionally, the concept of a "transparent" filter is something of a oxymoron. Either you are going to affect your signal or you aren't, and everything will involve some compromise. For instance, better filtering in the frequency domain may result in poorer performance in the time domain. Choosing what you can "ignore" is key to a good design.