When it's something like exercise, it's a bit easier to power through that inner voice. I can feel that and it might persist through the entire workout, but it's doable. I don't have to think about much, just have to perform physical tasks. It also does help "clear up" my brain in a sense, much like sitting in the shower does. This can create better results for other tasks that require more brainpower, though the effects don't really persist very long after I stop exercising, unfortunately.
Sometimes starting on tasks that require my brain to work with me can be enough momentum to push start it into whatever it is that I need to complete. But a lot of the time it is exactly as you describe; no matter how long I work at it it's extremely hard to get through or even impossible. If my brain doesn't want to retain information or process information to create something, it won't.
There are strategies and things that can help with this, but a lot of them require external resources and understanding. Having well defined tasks with good external accountability can be really helpful. Having strong incentives for completing tasks can help too. The problem is that finding people that can accommodate your needs here is pretty damn hard.
It's going to be different for everyone that has executive dysfunction, but I think essentially it comes down to people chasing dopamine. Their brain desperately wants it but doesn't produce it in amounts that a neurotypical person does, making certain tasks much harder to complete (or conversely, allows you to really focus on something that for one reason or another is providing you it.
So the strategies for making something that is difficult to complete needs to feed into your motivations.
If you find yourself procrastinating and being unable to complete a task until the deadline is very close, but somehow find the motivation to complete that task inside that short window of time, then accountability is a factor.
If you have a manager at work, for example, and they are willing to help accommodate you, frequent check ins for accountability could help. They should be nonjudgemental, but frequent enough to make the task feel urgent. They could also break a larger project into small tasks (like a kanban) and have micro-deadlines for specific tasks rather than a deadline for the entire project. For a student this might be asking the professor to have check-ins or breaking a larger project into smaller homework assignments due daily.
If you're by yourself or people supervising you are unwilling to accommodate you, then the biggest favor you can do for yourself is try to break down a task before you start doing it. A project like "clean your room" is very vague and perhaps daunting. But if you break that down into individual tasks, such as "remove all clothes off the floor," "put all cola cans in the recycle bin," "take cups to kitchen", etc. it can be more manageable. Doing this also creates a potential reward system which you may or may not respond to: checking off a to-do list. Some people find this very satisfying and watching things get crossed out or checked off or deleted might just provide the dopamine that your brain needs.
Rewards are also a very important aspect to finding ways to complete tasks you don't want to. A reward might be as simple as someone saying "I'm relying on you to get this thing done for me" or it could straight up be a tangible reward like money or food or whatever else gives you joy. If you can figure out ways to trick your brain into rewarding yourself, then all the better. Personally creating a reward like "you can play video games after finishing writing this bit of code" doesn't really work for me since I can very easily just go do that thing. Perhaps something like adding something to a shopping cart and saying you can submit the order when you've completed your task might work if you can afford it. Still, external reward functions work better in my experience, though even knowing someone else is relying on me to complete a task is a big motivator for my brain to get it done. Rewards also need to be frequent. Having a reward set up for the end of a project is not going to be useful for motivation throughout it. You need to have regular rewards built in for them to be really effective, I think.
Another strategy is to set a timer. This timer can be for whatever you want, but the thought process isn't just to do something for that long, but rather a challenge against the clock to see how much you can get done. If you're in the kitchen and you're microwaving some food for a few minutes, you could maybe use that as a timer to see how many dishes you can put away or wash. You can play a song and see how much of a function you can write in your code before the song ends.
Those are some of the ones off the top of my head, though there are probably more resources you can find online for dealing with ADHD or executive dysfunction that would help a lot.
I know it's a band-aid solution, but for me as someone with ADHD stimulants help a lot - but I don't say this to discount your recommendations which are effective. With stimulants, I'll usually find the right attitude or perspective to accomplish whatever task is at hand. If it's boring, I know I can find a way to automate or delegate its completion. If it's too exciting (too complex to be actionable), I'll redefine it to be actionable. If neither of these apply, I know it's something very novel and creative that stimulants will probably not help with its fruition.
Sometimes starting on tasks that require my brain to work with me can be enough momentum to push start it into whatever it is that I need to complete. But a lot of the time it is exactly as you describe; no matter how long I work at it it's extremely hard to get through or even impossible. If my brain doesn't want to retain information or process information to create something, it won't.
There are strategies and things that can help with this, but a lot of them require external resources and understanding. Having well defined tasks with good external accountability can be really helpful. Having strong incentives for completing tasks can help too. The problem is that finding people that can accommodate your needs here is pretty damn hard.