Hourly billing is a method of setting prices by looking at the cost of the product you are selling. In fact a customer does not care what it costs for you to deliver a product or service. You could be delivering a product that is made of diamonds and unicorn horns. It doesn't matter.
What matters is the value of your product or service to the customer. Your job, as a business owner, is to set your price based on the customer, not based on your costs.
Set your price based on the value that you deliver. Then adjust the inputs (hours of worker time, etc.) until you can deliver the value at that price. Mercedes Benz adjusts the inputs for a C-class car until it hits the target price. It adjusts the inputs differently for an E-class or S-class car.
There is a lot of information out there in the wide world about this. It is not "fixed pricing." Call it "value pricing." Fixed pricing is just computing the cost of your inputs, adding a margin, and declaring a price. Value pricing is a matter of working backwards from the customer's value desires to set the price.
For you math people, this is an "area beneath the curve" problem.
I'm an international tax lawyer. I make far more money (and have happier customers) when I charge a declared price than when I bill by the hour.
All that being said, one of the points in the article is exactly right: raise your prices and you will get better quality customers.
Go see www.verasage.com as a jumping-off point for discussions of pricing in professional service firms. All business are alike. Don't think that advice to an accounting firm is inapplicable to you. It's not. It's all "delivery of a service to a human being in exchange for money".