If your goals are unachievable in practice, maybe it's because they are defined as "yes | no", as opposed to "more | less". The goals defined as "more | less" are usually achievable; there is usually something you can do to get "more" of something.

Is there perhaps some goal or a part of a goal than could be converted to the "more | less" type? Or "better | worse" or any other continuous scale. (Make more money than now. Donate to charity more than now. Have better social relationships than now. Have more and better sex than now. Learn Chinese more fluently. ...)

Unfortunately I'm guessing that you already put in some really solid thinking on this, and that there's not anything easy I can offer to either suggest a desirable thing you've overlooked or to provide more evidence for achievability. I put together the supplementary post but I'm guessing (if you're asking this question) that you read it and it didn't help much, and that you have good reason to expect that LOTR won't help (and that for a variety of reasons it might well not).

But a few ideas that seem fairly easy for us to see the appeal in, and that we can generally do something to increase. Maybe you'll find something here that strikes you.

• Human beauty and sex. (To anyone reading this, I don't go in for manipulative PUA, but do endorse mutually positive, happy interactions.)
• Children. This one is kind of a stretch if you don't see the appeal already, but you might try exploring it. I didn't get this appeal for a long time, and then I imagined in concrete detail raising a son or daughter in a happier world, where I could devote my time to them (if it's appealing in this world too, then by all means). Showing them the world, teaching them things, seeing them grow, them running to me and showing me things, I thought to myself "holy shit, that sounds awesome". People sometimes mention incredible joy in the birth and existence of a child, and that they would give their lives for their kids, and these things don't seem to be bugs. (Not to say other feelings are wrong - there are different unconscious strategies for different assessments about our situation - but that this answer isn't flawed.)
• Survival, being alive. Life being way better than not-living, even if we don't see anything spectacular about it at the moment.

The following all happen to be about hypercompetent thinkers. How inspirational they are varies.

• Limitless. If you like the Bourne movies you'll like this. My favorite scene is when Eddie, the main character, is on the phone with his girlfriend while she is being pursued by a bad guy. It is a fun little dramatization of brains being mightier than brawn. (For me the main defect of the movie was that despite his chemically enhanced hyperintelligence Eddie does some stupid things in order to keep the plot wheels turning.)
• Understand by Ted Chiang -- available in its entirety online! This novelette is kind of a takeoff on Flowers for Algernon. Unlike in Limitless, the protagonist doesn't do anything stupid, yet the story manages to be interesting.
• R. Scott Bakker's Prince of Nothing trilogy. I started this on Yvain's recommendation but somewhere in the second book my interest flagged or I got distracted by other books or whatever. I'd still like to finish it sometime. From what I've read of it, Kellhus (a super-smart rationalist who is also basically a ninja) is kind of an antihero, or at least morally ambiguous. He's very good at achieving his goals, but I don't know whether his goals are worth achieving.

Edit -- here a couple other things:

• The main character in Frank Conroy's Body and Soul is a musician with a lot of native talent (who also puts in the hours). I recently typed out a favorite passage.
• A bit different from the above stuff, but Wodehouse's Jeeves stories are laugh-out-loud funny and feature a hypercompetent valet. (I know these from the stories rather than the TV adaptations, but the latter feature Hugh Laurie and Stephen Fry.)

I am primarily referring to the unconscious drives underlying our actions, not our verbal goals. No matter what term I used to describe it, when I imagined myself doing very well in general relative to other people, spending every moment in focused and topical optimization, I was excited and driven to pursue the things I expected to make me like that. If I anticipated outcomes that did NOT involve me being that kind of person, there was far less unconscious drive to act.

Being hyper-competent was not a subgoal of programming or business, and if it were I would have your same critique. Being hyper-competent was a subgoal of having social success, having riches, being safe, a general assessment of "able to succeed even in difficult situations." Programming and business were rather what seemed consciously to be the best specific routes for achieving these things, but they involved not being the sort of hyper-competent person, and because I unconsciously desired that so much I was not, in practice, driven to pursue programming or business.

Similarly, unless you have already developed high competence in many concrete tasks, how would you recognise a mind that was a perfectly honed instrument for realizing your goals?

The term "perfectly honed instrument" is meant to convey an intuitive sense, not a technical description. But you would recognize such a person by them constantly engaging in what actually seemed to have the greatest marginal return on time, and probably by quickly developing unusually large amounts of skill.

Taboo "perfectly honed instrument", "hyper-competent" etc., and the goal dissolves.

Those terms refer to particular patterns of reality and not others - Bourne, rational!Quirrell, arguably rational!Dumbledore are all extensions of this intension. The average person is not.

Going up the pyramid of goals in such a context is an active hinderance, because the higher goals are harder to make operational.

By "going up the pyramid of goals" I'm referring to understanding more precisely the rules generating the particular, concrete situations we desire, and following a rule higher up on that pyramid. In other words, are there some things we could think of concretely, that once thinking of them, we realized were the real reason we had been motivated by something else was that we unconsciously anticipated it to lead to the first thing? This is something for each person to discover on their own, but it is something to discover.

"Beware affective death spirals on far-mode (sub)goals" or "Taboo specific terms in your goals to make them operationally useful" or possibly even "Check that your stated goals are not semantic stop-signs"

Are you doing those things already? Do they leave something left for you to desire in your rationality? These are all descriptions of much more surface-level techniques than what's being discussed here. This technique is about finding concrete things that make you think "hey, that's awesome, how can I get that?"