The crossbow, mule, and gem prices of course carry over directly (the crossbow and mule are even listed in the Rules & Magic book at those prices). But that has nothing at all to do with the worth of the gold crown, not even by comparison.
If converting value-X from value-system-A to value-system-B result in value-Y, then value-100X should yield us value-100Y.
In the gold standard system, you can easily say that a gold crown is worth 500gp (despite the fact that there's almost certainly nowhere near 500 coins worth of gold in the crown, by weight*) simply by saying it has good/decent craftsmanship or other adornments etc.
*For reference, I base my estimations of coin size/weight roughly on roman coins, or approx 3-4cm in diameter, and approx 2-3mm thick
Assume the crown's value were given in how many crossbows it is worth - say, 20 crossbows. To get how many gold pieces or silver pieces the crown is worth we only have to multiply 20 by the individual price of crossbows: 500gp in gold standard and 500sp in silver standard.
Conversion can only be done successfully, if the individual items converted have the same ratio of value compared to each other; otherwise, it is not really conversion but revaluation.
At least, that's my opinion. I must add that my approach is based on gameability and has absolutely nothing to do with historic reality whatsoever (just as RPGs themselves).