You're far too kind, Jim, as always
Anyway, regarding the templar's attribution and not wanting to interrupt the interesting discussion going on, I think that the things to consider are rather simple:
- Let's check what kind of cross was being used by the Templars at that time at that place, and see if it was exclusive of them.
- Let's check if the cross in the pommel conforms with the typology of said cross.
If it doesn't, is much more probable that the sword belonged to just a good Christian, fearful of God, who wanted a cross in his sword for religious reasons. In the chaotic scenario of a battle, every bit of possible help is always welcome (there's a reason why sailors and soldiers are such a religious bunch, in general. As religious as superstitious, in fact. It tends to happen when you routinely put your life, literally, in the hands of fate).
In short, if we can't clearly say it's Templar (found in a Templar household, for example), with some kind of proof, it probably isn't. Templars were supposed not to adorn their belongings (another thing is how hard was this rule really enforced at that time) and, at the end, even demographically speaking, there were not that many of them, compared with regular knights, no tot mention plain soldiers. Of course, there was a much larger amount of people associated with them (servants, workers, etc...).
Unless the cross is clearly templar, and the templar cross wasn't used by a significant amount of other people at the time, I think the templar's attribution isn't really warranted.
Just my opinion, of course