I am painting the same Mirliton Late Crusaders as Hospitallers, though I am keeping them as a small DBA army while I finish my first Carthaginian FoG army.
From what I have found, the Hospitallers started to shift from the black and white design to a red with white cross at some point in the middle of the 1200's, but I have not found any conclusive date for when this started. It seems to have been a way for the actual knights to distinguish themselves from the sergeants and other non-knightly soldiers.
I'm doing a mixture where the Knights wear red with white crosses and the rest wear either black with white crosses (sergeants) or white with red crosses (members of other orders). I'm not sure how completely historically correct it is, but at least it makes your knights stand out even more!
http://tutorials.livinghistory.ie/Home/ ... ospitaller
EDIT:
Painting and Heraldry
In Outremer, the Hospitallers were distinguished by their black cappa clausa, a long monastic cloak with slits at each side for their arms, and bearing the device of a white cross on the chest. Recognizing military convenience, Pope Innocent IV authorized use of the lighter surcoat in black with cross in 1248 AD. In 1259 AD, Pope Alexander IV fixed the habit as a black mantle in peace time, and a red surcoat with white cross in war. Some Knights supplemented the red surcoat with a black cloak (as at right). The basic design of the cross was the eight pointed Cross Pattee-Nowy, known as the Maltese cross after the Order's relocation to Malta
The standard of the Order was a white cross on a scarlet field. Each of the Masters of the Order also had their own personal arms, which can be depicted on a banner. While still in Outremer, the rapidly expanding Order was organized by nationality into seven "langues" (languages) comprising knights from Provence, Auvergne, France, Italy, Spain, England and Germany. Later the Spanish Langue split into the Langues of Castile-Portugal and Aragon. The langues became a prominent part of the Order's organization after the relocation to Rhodes, and several survive as national orders in the modern age.. Each langue had its own commander ("pillar") and its own inn or hostel ("auberge") within the fortress at Rhodes. Each langue was assigned responsibility for maintaining and defending a portion of the walls, which proved ill-advised in that the sectors controlled by the smaller and less affluent langues provided vulnerable. In any event, the langues offer the opportunity to personalize your army, since each langue purportedly used a different color cross to distinguish its members: English (white), French (red), Auvergne (green), Germans (black), Italians (yellow).
http://www.fanaticus.org/DBA/armies/IV56.html