"Polish 13th cent crusader crosses? " Topic

I'm creating a Polish retinue for Lion Rampant Northern Crusades, 13th century, and was wondering if there was a "Polish cross" or other insignia that was used by Polish crusaders?

White eagle on a red background,(Gules, an eagle argent, armed, crowned and beaked or, langued argent) possibly from around 1000 (bird on a coin), definitely 1295 onwards, Arms of the 'Piast dynasty'. They were pretty much anti Military Orders, particularly the Teutonic Order (which was eventually absorbed by the Polish Commonwealth in the late 1600's). They both wanted Prussia and Lithuania.

If they were crusaders, then it would be their family arms with a latin cross sewn on to their clothing, but not on flags or painted on shields. Polish arms were quite simple and belonged to all members of the same family. They did not change much (if at all) over time.
The Polish royal arms are a little bit more complex than described above (you can find pics of all arms on the interweb).
Only some of the lands of the Order were taken by Poland. The Order had impressive land holdings in the rest of Europe and is doing fine and dandy (if a little less important) today

Thanks!