@Nyrryl-Cadiz unfortunately there is little room for negociation regarding to the schedule. This current book is going to printer some time in January I think, and it will be out in the market in March 2020.
Thank you for the input. My first instinct was also to limit research time, and cut back a bit thumbnailing time. What I did so far is I look for a decent idea for each rhyme (using mostly keywords, and doodles), and once I found a decent idea, I will still do a couple of thumbnails to get a better composition, but I stopped to explore ideas in complete different directions. But then @Lee-White 's voice is in the back of my mind - "you need to do enough research/messing around" , and also @davidhohn 's voice saying "do not go for the top card solutions, because that is most of illustrators do."
I am still in the process of thumbnailing and rough sketching for the entire book. I just want to check with the community if anyone has other tips for such situation.