On the contrary! I'd say Intuitives probably have more patience in writing to work with than their Sensate cousins. Your problem is likely that you're an Extrovert and don't like to spend a whole lot of time alone.
Obscure psychological theories aside, let's cut to the chase.
I just want to spend that time thinking more than writing.
Okay. You're not going to get out of writing completely, so let's find a way to make it more bearable.
I think you should start by outlining the story(ies) you have in mind and writing down all your ideas, to see what you have to work with. The thing is, writing is very nearly the same as thinking anyway if you're doing it off the top of your head. You need to get used to your keyboard--actually, make sure you're consistently working at the same keyboard. Writing will feel a lot less tedious when you're pounding it out at 70wpm, so practice and patience with typing will make it a lot easier.
A vague representation of the general consensus on the stages of writing or whatever blather the pundits are putting about these days:
1) The ideas: as you say, designing it. Coming up with the world, the characters, and the plot. Worldbuilding and outlining.
2) Starting to write. You lay down your characters like cards in that ridiculously nerdy game you played all the time twenty years ago (not last week at all, no).
3) Revising. Nearly everyone hates this, but you have to do it.
4) Editing. This is really easy, actually; if you disagree with me, go find someone who doesn't.
For you, I suggest skipping most of the first step. Keep your outlines really rough, worldbuild as you write, and just keep another Word file with all your notes.
Personally, I don't like marathon worldbuilding sessions, and I find I come up with my best ideas during the first few chapters instead of before starting to write, and since I don't like going back and altering all of my notes, this is what I do.
But there are multiple reasons to write that way, one of them being that you think the actual writing part is pretty boring and just like laying down ideas. Once you don't have to think about your typing, the writing part just becomes worldbuilding with organization.
Also, I know it's said a lot, but if you're still new to all this, don't expect to be immediately good at it. Some people say--and I think this is pretty accurate--that writing takes about ten years to learn to do well. I'm halfway through that, though the first of those years was spent writing about trigger-happy alien fairies who had an obsession with the color yellow, so I'm not entirely sure that counts.
Anyway! Basically, don't be discouraged, because the first crepe goes to the dog. And, in writing, the second, third, fourth, and fifth, and then the sixth you just kinda cover in powdered sugar and serve because the dog is bloated.
Sheesh! That was longer than I intended it to be. If this is a completely unhelpful, rambling waste of the past five minutes of your life, let the record show that I do not claim to be an "expert," "professional," or any other silliness. Actually, I'm a 15-year-old girl with an extremely vivid imagination and a vocabulary that gets me funny looks. There! Now you've been spared the feeling of being lectured at by someone who sincerely thinks s/he knows what s/he's talking about, and is actually way off base. Isn't that better?