Nor is there a law of physics saying "your subjective point of view immediately blips out of existence and is replaced by Someone Else's point of view if your spacetime coordinates change a lot in a short period of time (even though they don't blip out of existence when your spacetime coordinates change a little or change over a longer period of time)".
I feel like this isn't a fair comparison, as if I were cloned completely and relocated (teleportation), I wouldn't expect to experience both original me and cloned me.
The best analogy I can think of is as follows: You have a camera recording constant video. If you were to clone this camera exactly, you shouldn't expect camera 1's storage to start recording camera 2's output, even if the two cameras are perfectly identical but in a different location.
It is much harder to motivate myself to exercise, for example, because it is a painful task with no reward in the near future.
When the reward is the reason you want to do something you don't want to do, why do you care about the reward?
Imagine a man who lives on an island large enough to sustain him. In the distance, he can see other islands and has heard from passing ships that they hold great wonders, which sounds great. Problem is, he can't motivate himself to do the work to build a raft and travel over because his island already has everything he needs. Then one day a fire wipes out his farms, leaving only whatever food he has stored away untouched. Now, assuming he cares about living, motivation to build that raft is a lot easier to find. The action (building the raft) and the reward (reaching another island) haven't changed, but the reason he wants those things (curiosity --> not starving) has.
Back to exercise, if the reason you want the reward of getting stronger is because you've heard detached experiences from other people about how cool it is, it's unlikely that's going to be enough to motivate you. If, in your current situation, you don't have any real desire to be stronger or healthier, say you're healthy enough or have never needed more strength, the pain of exercise sounds crazy, why would someone subject themselves to it? Then a day comes where you experience some event which takes these abstract notion of strength and health and molds them into a clear, relevant goal. Maybe you were mugged and hated that feeling of being powerless, maybe someone close to you dies because they had weak lungs and you fear a similar fate, that link could come in many forms. But without the link, whether made through trauma, curiosity, or a goal, it's not that you don't care about something but rather you don't even understand why you would want to care about something, which makes it very hard to bring yourself to do it.
This idea of finding something to care about and pursuing it is what the sequence I recommended talks about, but there's a chance the angle it comes from won't be helpful for you based on how you've described things. I've found the more ways something's explained, the more likely one of them are to stick, so I hope this helps if the sequence doesn't.
Why bother with effort and hardship if, at the end of the day, I will always do the one and only thing I was predetermined to do anyway?
Say we plug in a specific example here: "Why bother making breakfast if, at the end of the day, I will always do the one and only thing I was predetermined to do anyway?" Answers may vary, but I imagine most will boil down to 'Well if I don't I'll be hungry/tired/unpleasant feeling, and the effort it takes to make breakfast is worth avoiding those feelings' or the inverse "If I do make breakfast I'll be full/energized/pleasant feeling..". This question has different answers based on what action we fill in, but all of them rely on what you value/desire to be answered. Motivation generally comes from the expected or desired outcome of an action.
It seems like your issue may not be determinism taking away your drive/'responsibility' to do something, but rather your comfort/complacency with the current state of your reality, similar to the senioritis a student may experience. If the only reason a student is studying in class is to get an adequate GPA, once they've learned enough to acquire that GPA, there isn't any reason for them to continue as their goal has been met. Conversely, a student who is pationate about a subject isn't motivated by an external stimulus (GPA), but rather intrinsic motivation (their desire to learn more).
I'd recommend reading So8res' sequence on Replacing Guilt, but if you don't have that kind of time You're allowed to fight for something and Half-assing it with everything you've got were the two articles that hit home and helped me break out of a similar mindset of pointlessness by revealing that there are things I care about/worth the effort.
This feels like a typo, maybe "You are lucky I am cleared.."?