Hm... I've seemed to amount more than a fair share of Sphagnum in a year and a half of growing it. I haven't focused much on making it grow rapidly because every form I have grows pretty much at the same rate for me. Here's information I've gathered on growing it, if this helps any...
I've found that if the culture has too much water in it, the low areas of the culture will decay.
One thought I've had was to having flowing water through it, rather than 100% stagnant water in culture medium.
I've been to a big lake (2-3 miles all the way around) where the banks are covered in thick Sphagnum.
However, the only banks that are covered are the areas with slowly-moving water or areas that are protected by the wake from boats or streams flowing in.
I think it would be awesome if you were able to have cultures were the water circulated very slowly (maybe a drip line with a low-pressure stream of water trickling out of it, then draining through the bottom,
being filtered and re-trickled into the culture.
On the same lake, looking very carefully along the path that runs 5-10 feet away from the bank, the only area I've found Sphagnum was a tiny, tiny rock face (a couple square feet) on the side of a hill where water trickled down from runoff (like during rain)... However, that was a similar but obviously different species of Sphagnum growing there.
Maybe the best thing to do would be to replicate the exact conditions of the location you found the Sphagnum at. But that brings up another issue, because all Sphagnum grows in different conditions. I suspected that the lake I found all of the Sphagnum growing at was a high-nutrient water. It obviously wasn't deprived of nutrients because there were tons of deer in the area, tons of fish in the lake, frogs that probably expel waste in the Sphagnum, not to mention all of the tiny bugs that live in the Sphagnum and die in it. That species of Sphagnum could probably tolerate higher nutrient levels than in a nutrient-low bog. Also, it was growing under the shade on trees growing along the banks and in the shallow water, so perhaps it would grow better in low light levels than Sphagnum in a full-sun bog would.
Also, another thing that was told to me on forums is that any red Sphagnum I got would turn green within a few weeks in my conditions. I found that to be untrue, even through the winter. I have one species that stays multicolored all year, never full red, but it has a bit more red/orange in there than it does green. Another species I have is less red and turned green for a short period of time before it grew in to fill the culture (which only took one summer). I also have a species that was purple and it turned fully green, and although it is a slower grower than the other red species I have, it has pretty much filled out the culture in one growing season and it is starting to turn purple again.
I don't have any specific references because there's literally no information online other than how to start a culture for beginners, or a rare dichotomous key for a few select species, or a short wiki page for a species of Sphagnum. You best bet would probably be the documents you have or by information given to you by growers.
IIRC WireMan had a document for identification of Sphagnum species in some state like Connecticut or something... Since he doesn't even live in that state and he has access to those kinds of documents, you might want to PM him and see if he has any references he could send to you.