It might just help to reframe what you think about reading. It seems to me you've decided that reading is a chore, work something you don't like doing for some reason.
If you reframe that idea and decide you love reading then you'll find yourself doing it automatically. Also be wary of the target you set yourself... your ambition to read many books could be unrealistic given the other activities that you might already have in place. This will set up blocks that have you avoiding books altogether.
If you enjoy reading you grab a book and read when the moments allow. It isn't an issue for a reader to 'have to' read a book, they are around when we have the 10 minutes or so to photoread and postview, later the 10 - 20 minutes to activate that book once and determine if we want to know more another 10 - 20 minutes later. Then along comes a book we know we are going to sit down and activate asap.
Your project sounds like you're punishing yourself rather than rewarding yourself. If it is a reward to read many books during summer then nothing will stop you. Ask yourself why you 'really' want to read so many books. Is it just to "show them'? Or is it because of the rewards you can enjoy of knowing how much fun you have reading?
Alex