Typical phrases, clichés and everything that a customer hears a hundred times a day, even not from you, do not work. They are pointless not because they sound ugly but because the customer knows that there is nothing behind them, they are fake. There is no honesty and no real apologies behind these phrases, and as you know, hypocrisy does not evoke any warm feelings. As soon as you move away from the clichés and add personal details (inside information on what has happened, the details that are specific for this customer, etc.), everything changes.
The purpose of apology is to show that there are humans on the other side. If the company made a mistake or did not foresee something, by saying sorry, you demonstrate that you admit there was a mistake in the past, and your understanding and recognition of the mistake is half way to rectification. By saying sorry, you show the customer that you are on his side, and you are involved in the looking a way to solve the problem, demonstrate empathy. The official language and standard phrases are not suitable here. Every apology is a unique message addressed to a particular customer (still it can be based on a template if you have a good one, but always amend it by adding the details for a specific customer).
To learn how to do this in a quick and effective way, you may need to spend some time and get more practice, and be ready to try the new approach on the customers.