Thinking further about Henry's motive regarding William's promotion, I found it interesting to re-visit ch.24. At this point Henry has started to become more seriously attracted to Fanny. He has been listening to William recounting his adventures:

His heart was warmed, his fancy fired, and he felt the highest respect for a lad who, before he was twenty, had gone through such bodily hardships and given such proofs of mind. The glory of heroism, of usefulness, of exertion, of endurance, made his own habits of selfish indulgence appear in shameful contrast; and he wished he had been a William Price, distinguishing himself and working his way to fortune and consequence with so much self–respect and happy ardour, instead of what he was!

The wish was rather eager than lasting. He was roused from the reverie of retrospection and regret produced by it, by some inquiry from Edmund as to his plans for the next day’s hunting; and he found it was as well to be a man of fortune at once with horses and grooms at his command. In one respect it was better, as it gave him the means of conferring a kindness where he wished to oblige.

I think this passage shows that Henry respected William Price and wished to oblige him, so his motive in arranging William's promotion was not solely to please Fanny and gain her good opinion.