Hello and welcome,
I believe how much mechanics you include in your write-up depends a lot upon the purpose for your written record, but if you are intending to post with a strong focus on entertainment value, then you are correct, some kind of balance between story and mechanics needs to be met to satisfy most readers. My enjoyment in reading solo-roleplays comes not only from the story but also from learning new systems and tools and seeing how the author uses the various random tools to shape their tale. If there is too much mechanics, then it does bog down the story and most of the time large strings of numbers or dice rolls become meaningless. However, if there is little to no description of mechanics, I tend to lose interest because then I am just reading a story like any others you can find on creative writing sites. (Also, I can't help but wonder what is the result of a die roll vs. the player's
divine input.)
This is how I typically handle it. If it is the first time I am introducing a mechanic into a game I will usually go into more detail in listing the rolls, possibly even going into extra detail to explain how the mechanic works. When it shows up again, I use shorthand or possibly even leave it out altogether. In the latter instance, it's either a mechanic that has come up several times before or I've indicated previously that that mechanic will be used in similar situations.
Another thing I do is put the mechanics in a different font style, such as
[bracketed purple italics]. It takes a bit more time, but that notifies the reader that the text is informational and not part of the narrative. If they are not interested, it's easier for them to skip it.
There are few more ideas, but those are the big two for me. I would suggest looking at a few writers who I feel do a good job balancing narrative with mechanics. Besides myself (at the risk of self-promotion) I would suggest Jingo's stories posted on this site. Another good example is Gerard Neval's stories over at
http://aleaiactandaest.blogspot.com/. While I'm sensitive to directing people away from Mark's site, I believe this author is one of the best I have read and I have learned a lot about writing solo-roleplays from his site. There are other good writers on this site and a lot of different styles. Read some and see what feels good for you. If you have any questions feel free to comment or send a private message.
P.S. In regards to your last point, for me, recording my session and writing the narrative are two separate documents. The game record includes every die roll, random generation, and any other notes to help me remember what happened or ideas I have for the final story. The narrative is the version that will be posted and distills all that information into a more readable form in order to tell an interesting story.