I know that the predominately Christian kingdoms of the medieval Iberian peninsula were mostly concerned with the Reconquista, but is there evidence that Castile, Aragon, etc. participated in any of the major (numbered) Crusades in the Holy Land? Or perhaps evidence of a contingent of individuals from Spain serving in a religious order or under another king in the Holy Land if not officially in the service of their own kingdom?
Various military actions of Portugal, Castile, and Aragon were nominally sanctioned under the Second Crusade, but as far as I know they were all undertaken inside the Iberian Peninsula.
No.
When the Crusades in the Levant started in 11th-12th centuries, Christian kingdoms of Iberia had been involved in their own conflict against Moorish kingdoms there and kept their focus on the peninsula. It was not until the 13th century that the Reconquista was considered to be on the Christian's advantage.
In the 12th century, a fleet carrying English, Flemish, and Rhenish crusaders stopped in Portugal on their way to the second Crusade in the Levant. At around the same time, Alfonso VII of Castile and Leon was able to gain Papal dispensation to cast the Reconquista as part of the second Crusade. So the northern crusaders helped Alfonso I of Portugal to attack and win the city of Lisbon, before they continued to the Levant.
The closest that an Iberian kingdom was to intervene in the Levant was when James II of Aragon promised his participation in Pope Nicholas IV's effort to bolster Christian forces following the collapse of Tripoli and the siege of Acre in 1291.
However, James II ended up negotiating a separate treaty with the Mamluks: he would withdraw his support in exchange of security for Aragonese pilgrims in Jerusalem.