If only he'd shut up and calculate, he'd realize that to prevent the largest amount of suffering he should dedicate his life to researching magical means of granting immortality to everyone, like the Philosopher's Stone.
Granting immortality is not the same as preventing suffering. Maximizing life span may in fact maximize the opportunities for suffering.
Future suffering or death must be discounted to provide a present value. It is more valuable to save a life now than to save a life a year from now, all else being equal.
Harry would also have to consider opportunity costs and the likelihood of success. He knows that dementors can be killed now. Finding an acceptable magical approach to immortality is less certain, and may actually take more time to develop than a non-magical approach. Harry's optimal approach may be to kill dementors now, research the nature of magic, and to wait for muggle science to find immortality.
I question the extent to which the two goals have to be juggled in any case, since he already knows how to kill Dementors, and isn't willing to throw his life away to destroy them, which would be the main conflict. Destroying the Dementors is now a tactical issue that need only concern him when playing politics, so the only way it interferes with his transhumanist goals is if his politicking interferes with his research more-so than it would have if he weren't doing it with Dementor destruction in mind.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: