As far as i can tell (on the spot, not a ton of introspection on the subject):
When speaking verbally i don't mentally experience it. There is no thought, the words are just expressed. When i'm searching for words to expand on ideas i have already spoken, there is often.. just nothingness. Eventually i speak it, but there is nothing that triggers this.. the words just come to my mouth. As strange as that sounds.
When not speaking verbally, i think in internal monologue. No pictures, just a voice that seems to be soundless (i can't tell if it sounds like me, i mean).
When i am forming an idea, such as a data structure in code, there is no way i can describe how i experience that. If i'm searching for how to design it, sometimes i'll talk with myself (verbally) and figure it out, but if i'm not talking in myhead or verbally, then it's this.. ephemeral idea that slowly becomes actionable, but never visually/audibly clear.
This is actually quite the interesting question to try and answer. Thanks :)
As I've become more involved in meetings at work, I've noticed a myself speaking like you describe. It's as though I've trained my hind brain on the topics being discussed and can just let it pattern match the conversation to generate and issue a response. Problem is I often don't even remember what I said, much less am able to build upon it when questioned.
The change has probably come about due to the pacing of conversation. I remember that before I'd build a statement in my head, test phrasing a couple different ways, check that it made sense in context, then say it. That's quite a bit slower, though, and often by then the discussion has mutated such that the constructed statement no longer fits.
On those rare occasions of deep, thoughtful conversation is when I notice the difference. Thoughtless speaking seems to be something I slip into, while thoughtful speaking is very deliberate - I have to consciously stop and force myself to actually focus on and consider the topic sometimes, especially if it's been a while.
Like maxhudson suggested, writing seems to me to most closely match the process of thoughtful speaking. Even if the first pass is on autopilot, you can go back and reevaluate, analyze what you wrote.
My oldest son thinks in pictures. He had a really hard time learning to verbalize what is in his head. It has gotten better, but he still sometimes makes errors similar to non native speakers, because he literally does not think in English and things sometimes get lost in translation.
I homeschooled him. I worked with him to help him learn to verbalize and I still serve as his sounding board on a regular basis. I also get a lot out of communicating with people. I do that a lot on the internet. Saying it in writing to other people gets fairly rapid feedback as to how effectively you expressed what you meant. (I went down in flames online a lot for a while. It isn't the most fun I ever had, but I learned a lot about what not to do.)
So, you need to find some means to more effectively access your thoughts and train up your ability to more rapidly translate what is in your head into spoken words. Because my son thinks in pictures, we used a lot of image rich sources to help him with that. He read comics and other illustrated works and we used educational sources like Grammar Rock and Vocabutoons to help him work on individual pieces of the language puzzle in isolation. He couod not cope at first with trying to put it all together.
So, find an educational source that resonates with you. It may not be image rich products. Maybe you will do better with audio sources or something else. But find something that clicks for you and start working on individual pieces of this.
If you can find a person to serve as a sounding board, that might be a good thing too. One means to do that might be to get a jogging buddy. Talking side by side is a very different experience from talking face to face. My sons and I live without a car, so we spend a lot of time walking together to get around. It fosters good conversation.
You see this phenomenon as well in cars. People sitting next to each other are more comfortable being chatty than people face to face. You see this phenomenon play out with how people talk with cab drivers, for example.
