It seems to me that an important part of your message is that you want to preserve your relationship with your client, but not jeopardize your own interests.
I would suggest asking yourself: “What happens if I name my maximum price and the client refuses?”.
If it doesn't cause anxiety within, bid the price without hesitation or doubt.
If there will be anxiety and regret, here I suggest this strategy: voice your price without discounts and listen to his reaction.
There are two possible outcomes: the client agrees - and you calmly start work, or he refuses. In this case you can say: “I am interested in cooperation, what can I offer to make it mutually beneficial?”.
After that, you can discuss options: for example, lower the price, but with a limit on the number of edits (up to two or three) or with minimal adjustments. This approach will help to maintain a balance between your interests and the client's wishes