this is really hard to say as a non-tutor ^^
but let me say things like this:
수줍다 is also describing the smile, Yes.
Or we can also say we can imagine a girl smiling who is shy ordinarily but she was showing a smile we could barely see from her.
You can see a phrase out there like "수줍은 너의 미소". This is the simple example using 수줍은 + 미소.
But the above case, it's using "수줍기만 하던". I use this when I remember something. something in the past in my head, in my memories. But you can say this at both situations you can see the person in the future again or not. It doesn't matter. Of course this has the same meaning with "수줍었던 미소" as in that it is describing something in the past.
Lyrics is difficult ^^ it's like a poem. When I saw these lines first, I imagined...
1. this person would be a boy or a man.
2. maybe he met this girl first time at least days or weeks ago
3. they are quite friendly now but not that close as lovers
4. he hopes they become more close since today
'도'...it means "as well"
In this case, it stresses they are not as friendly each other as he wanted, but since today it will change. Actually he wants it to be changed.