I have long since decided that my intended corset would be burgundy, simply because I love that colour. The coutil is dyed but I had some concerns about whether the colour would be historically accurate or not. An internet search alleviated my fears though. For the time period I am aiming for, colourful corsets were not unheard of.
So, no longer any doubts about the propriety of a red corset. Additionally I now have a lot of inspiration for embellishment.