in order to really give advice, I'd need to know how this situation happened. Doing a finished book by january is not really practical by any standard. Normal turn around times for a book is a year. When it's rushed it's 6 months and the fastest deadline I've seen is 4 months.
So, how did this deadline happen? Are the sketches done and approved? Did they just approach you for this job? Or did they sit on sketches for a long time before approving you to go to final. If either of these is the case, then you should push back VERY hard on the deadline. Push for a April 1st deadline or later if possible. Many publishers will push their books to the following season if it's behind schedule. And this one is definitely behind schedule. I just turned in final art for a book that is coming out fall of 2020. So this one coming out in March 2020 is not realistic at all. So it makes me wonder if they know what they are doing? Is this a publisher or a self pub.?
In any case,, I would STRONGLY advise making a case for a fall release. They are asking for trouble trying to hit a march release. Even if you get the book to them mid-jan., they still have to get the book to printers, get proofs and edits, and then do the actual printing. That process can easily take 8 weeks of time. Then there is shipping, etc. to stores, etc. They are asking for trouble with this timeline. And everything will suffer trying to hit that deadline. Art will be weaker, printing will be rushed, fees will have to be paid to hit those times.
Good luck, I don't envy this situation. If you have to do the art, I'd tell them what time you will need to really do your best work. If they say they have to have it by mid jan, think about using another name on the book and just banging out something that you don't care about just to get it done.