Will the suitor be rewarded for being the cause of a girl he wishes to marry wearing the hijab, and should he continue his attempts or choose another girl who already wears the hijab?

Whoever sincerely invites another to obey Allah and His Messenger will be rewarded, whether the invitee responds or not, because the act of inviting is an act of obedience. If the invitee responds, the inviter will also be credited with the reward of their response. The Prophet (peace be upon him) said: "The one who points to good is like the one who does it," and "Whoever calls to guidance will have a reward like the rewards of those who follow him, without diminishing their rewards in any way." If you discern that the girl is ready to become righteous, then continue inviting her according to Islamic guidelines. If you discern her obstinacy, then seek out someone else.