LondonLivvy That is so hard and no-one would judge you for considering it but please please please listen to Bora! I am doing a degree in Early Years Care and would never recommend leaving a baby to cry. Crying is your babies only voice and they need to know that you will come. It is an attachment issue. Someone upthread (sorry lost track who it was) mentioned that they work with abused kids. It may not be anywhere near this level but it is damaging.
The thing is we live in a society that calls food, warmth , cleanliness 'needs' but emotional comfort is somehow seen as a luxury we should grow out of asap. Pardon me for being blunt but what a load of balls! If your baby is crying to be cuddled it is because they NEED to be cuddled.
Attachement Theory (which is evidence based and widely accepted and respected!) states that if you always respond to your child's needs they will be more confident in you, with a secure attachement and therefore will cry less. Research shows that children who are left to cry actually cry more until it gets really serious, and they give up completely.
Sleep training is not reccomened until at least 2 years of age (sorry!) and even then, go for something like 'pick me up, put me down'.
The book you mentioned will work, but your baby will be learning that when they cry, no one comes. I wouldnt want my children to ever think this. They will learn to self settle in due time, with a supportive parent alongside them.
There is also some evidence that children who are sleep trained need to be re-trained after every change or major even in there life, whereas children who sleep through when they are developmentally ready dont regress back again.
None of that actually solves your sleep problem though so lets focus on solutions!
What support do you have in RL? Does you partner do the night shift sometimes? Is your baby BF or FF? Do you have other children to care for in the day or a job to go to? Sorry to bombared you with questions but I dont want to make suggestions that you cant follow through!