Goos one Moshe!
I think solos undergo the same changes as songs do. The way they come out depends strongly on your current mood. Sometime you are more sensitive so you might concentrate strongly on melodies and so on. The good thing about this is that when you listen to your solo later on you can exactly determinate in which mood you were.
Every player has its stlye so that you definitely find certain self-repeating criteria.
Singing or humming is a good way, but every guitarist suffers from one disease which is called the "I can not lay down the guitar and concentrate for a minute on the melody". We like to solo to loops and it needs a high level of discipline to work a solo out! It took me a long time to understand this.
As you described, you improvise and record yourself and later on there are parts that you like and parts that you dislike. That is just a normal thing. Hearing yourself play is a wonderful thing. Most of the things you play you will only realize when listening back to your recording. Of course you will then figure out that there were some cool parts.
I personally like those beautiful ideas that pop out on a first take. My approach is to keep them and to listen back to them. Then I start working them out, practice those phrases and rerecord them let us call this working off the rough edges.
Constructing a solo for me is chosing a mood or realizing the mood I am in. Figuring out if I will be satisfied by playing melodiy lines or if I need some shred in the solo to let to unleash the beast. What type of music am I soloing to? Shred over blues, Metal over pop doesn't really work for me.
A very important thing is the choice of guitar sound you make. This will strongly influence your playing.
Take yout time and don't push yourself. Do it step by step. A method I use is to set milestones. I do not automatically start at the beginning at the solo. Sometimes I feel a part of the solo fits better at the end of the rhythm ttrack, so I play a little puzzle.
Be creative and always keep in mind that the guitar is a dangerous tool to express something with a solo. A solo is no ego show
Try to find out the following when you tend to stuck:
sound+rhythm+dynamic+style+length+intention(just a fill or main solo) and so on