How to show special respect to a famous PhD advisor?
I don't know what field you're in, but in mine, writing such a paper would be viewed as unnecessary and perhaps a bit strange. You seem to feel that you don't deserve your place with this supervisor, and so you need to prove your worth, or impress them, by writing a paper. This is unecessary, as you have already impressed them with your project idea and PhD application. They would not have taken you on as a student otherwise. Along these lines, you might want to search the term "impostor syndrome", both on this site and on Google.
"I am exhausted...". The last thing you need to be doing right now is writing an unnecessary paper with no help from anyone. A PhD is a several-year-long marathon, and you will need all your energy and stamina to complete it. Take a break, rest and recharge before you start. This will have a far greater benefit to your PhD, and accordingly to your relationship with your supervisor, than writing a paper.
Once you have started the PhD, show your current paper draft to your supervisor and work on it together. The paper will be much better for it. Again, this is field dependent, but in mine it would be extremely rare for a beginning PhD student to be capable of writing a publishable paper entirely on their own. You may be underestimating the challenge. This is something that your supervisor will help you with.
But for now, have a holiday, and celebrate your success at being accepted for a PhD with a great supervisor!
I have worked with supervisors who are very humble while successful to those who are extremely egoistic due to their accomplishments. In my personal opinion, it is not wise to give Godly status to any person. He is your PhD supervisor, a famous one, but there are thousands of famous people in this world. And fame is subjective. Be professional, be polite and show respect. Do not overdo it as it might cause following issues.
Your colleagues will show distrust in you if you eulogized him, especially if they have a poor relationship with him. By keeping it completely professional you will less likely belong to a specific group in your lab. Same is with other potential supervisors and co-supervisors.
The 3 year PhD journey is not small. There will be ups and downs and without a doubt, there will be times when you will feel poorly treated or exploited. Those time will feel more awful if it comes from the same person who you eulogized.
Most importantly, you must keep your research above person. Write a paper because it needs to be written. Because you want to convey your findings to the community. Not because you wish to impress your supervisor or prove to yourself that you are worthy of doing research. You would end up doing a poor job in your research with that mindset.
You supervisor is just an ordinary human being who did some good research work. There are millions like him. And in a few years, you could be one too.
Even though you have not indicated where your Ph.D. studies are going to be, it is clear from your description of your advisor's behavior that he is not expecting special deference to him.
I would say that the way to show him respect is to trust him when he says "don't do that." Then learn as much as you can in the program, and accomplish great things in your career. That is what he ultimately wants from you.