I took your advice @yuriythebest and had a coffee while I read about your experience with the harmonica, which seems to be similar to my own.
Now it’s your turn to grab a cup of your favorite beverage!

Here is a little bit about my experience with the harp:
I also was very troubled by the fact that we can read tabs, which tell us which note to play, but nothing about what rhythm to give them. The answer, of course, is in musical notation, and the way you suggest is excellent, showing the harp tabs and the tablature. Nevertheless, my mind still has trouble translating what I see into something that sounds decent on the harp. While following tablature, of just about any sort, I find myself playing without much feeling, just mechanical blowing and drawing.
What has worked more for me is to just try and play what my mind hears. I’ve always thought that if you can hum or whistle a song, you can probably play it on the harp. I believe @Luke says something similar in one of his posts.
I’m coming up on my three-year anniversary of playing, and I doubt if I’ve played the entire tablature on any song for more than a few songs. It just doesn’t work for me to see all the numbers or the dots on the staff; but when I play the song in my mind, things start to come together. As a side note, I must admit that the songs I know from beginning to end, with intros, bridges and closures, are quite few. I’m mainly into the hook of the songs and solos which have been ringing around in my head since I was a little guy.
While it didn’t come all at once, little by little, the sounds I was hearing in my head started coming out of the harp. With the help of @Luke and others, I started to get more knowledge about how music works, and in particular, work on practicing different scales and positions.
When we listen to a song on the radio, or live, we can usually tell if there is a change from what we are used to hearing. It catches our ear right away and this seems to happen as I am learning a song on the harp. As soon as I find the starting point, I’m usually able to get the hook pretty quickly, and the rest of the song comes more easily from there.
I’ve got quite a few songs on my “Playlist” and while I don’t know the whole songs, I know the parts which most people sing along to and that make the song recognizable. It takes a while sometimes to work through some of the trickier parts, but in my experience, learning them by rote repetition somehow burns them into my lips, which memorize what they are supposed to do. I rarely think about if I’m blowing or drawing, and I almost never even know what position I’m playing, unless I consciously think about it.
Also, my expectations on my playing are probably a lot different from others. I’m not so interested in playing with a band or in public venues. Since I mostly “play with myself”, it’s all good, just so long as it sounds good to me, and this is exactly my point @yuriythebest …
I’ve watched you progress tremendously from your first posts, and I think you are doing great. What I might suggest to you is to think of a very well-known song and then try to play it on the harp without tabs. A good starting point is always the 4 blow or 7 blow, which start out on the major scale. From there, just feel your way through it. After that keep trying different places to start. The 2nd position is the next best place to start (2 draw or 3 blow or 6 blow), and then consider the draw 4 and the draw 6, which give you a minor feeling to the natural notes on the harp.
For example, today one of my nephews sent me the song “You Are My Sunshine”, with my trusty Baby Fat in Bb, within a few minutes of playing it. All this isn’t to say how great I am at the harp, because I’m still learning every day, but rather to give you another challenge.
Try Children’s songs, like Itsy Bitsy Spider or Twinkle, Twinkle, Little Star, or others you know well. I’m willing to bet that without tabs, you will be playing something that sounds pretty close in no time. Your ears will hear when you hit the wrong note, and you just keep moving up and down in the notes until you find the right one…
The kicker of all this @yuriythebest is that once you learn the song this way, it gets burned into your lips muscle memory, then it’s yours forever. Bingo Baby 
Hope this helps,
Harp on!