Disclaimer: This answer does not offer any help with decreasing shutter volume - it is an anecdote and therefore just a viewpoint that is related to your status quo.
I think that there is not much you can do about it - if you are aware that your camera is non-silent and you try your best to avoid it being disturbing, you already did everything you could. There might be others who have great suggestions to further reducing the noise output of your camera - but to me, the question remains if this really is necessary.
First, a few things about me: I would call myself an audiophile - I keep my music as FLACs (self-ripped from freshly bought CDs, of course!) because I really hear a difference, and I have a fairly decent audio setup. I worked as a FOH technician for quite some time and I love to hear the small details in music. I also like to go to concerts/the opera.
Lately, I was hired for some congresses and also a few concerts (and a baptism). Of course I did not want to interrupt people, as I would not want to be interrupted by those nasty click-sounds myself when I sit in a concert. However, I 'only' own an EOS 5D Mark III, and that got me worried, as DSLRs are not the quietest things on the market.
Even in Silent Drive mode, I always feared that someone would stand up and punch me in the face as the infernal sound of the shutter went on without any empathy towards the acoustic importance of the moment. However, the shutter sound barely gets noticed at all - I have yet to encounter someone that even turns around and looks at me. My EOS M6, which has a very distinct, high-pitched shutter sound, got me one or two looks when I used it in the Largo of Dvořák's 9th Symphony, but all in all, no one seemed to care much about it.
Then, on one occasion, another photographer was there - also with a 5D Mark III. We had different tasks, so we barely made photos at the same time, and therefore, I had some time to watch (and listen) to his work. To my astonishment, I could barely hear the shutter, even when he was standing a few meters away. Of course, that is quite a logical thing to happen: As the inverse-square law applies to sound intensity, with twice the distance, you only get one fourth of the volume. Therefore, something that is very close to me (like the camera, which even has contact to my face) might seem loud to me, but may be nearly imperceptible to someone just a few meters away.
Lately, I was hired to shoot some photos during a pre-recorded (as in: non-live) radio interview in a very small (perhaps 12m³), silent room. As I was not able to get good shots of the interviewed persons in a "fake" interview setting, I decided to get the shots during the interview - just over 1m away from the mic. If you ever recorded an interview yourself (I earned a living with that for some time), you will know that there is nothing more destructive than random noise during or slightly before/after the interview (you need some headroom, as sounds/voice do not die instantly, but fade out). The trick to not destroying the recording was to recognize when a person ends a statement - and take the shot in the small pause that occurs there. This probably required years of interview experience, a steady hand (and open ears) - and quite a bit of chutzpah. Eventually, I got the best shots of the day out of these shots - and the interviewer later said that while the shutter sound was audible, it was far enough away from the important stuff to be cut away in the final mix effortlessly. Please note that this was an emergency solution: Intervening in other people's work (which has higher priority) is something I try to avoid as much as posssible.
Also, it is much harder to make out the shutter sound when you do not know it is coming. I.e. if I fear the loudness of the shutter and I press the shutter release button, it will seem really loud to me, because I already expect the shutter sound (and it being loud). Unrelated persons usually do not even notice it, and they cannot foresee when you press the shutter, so for them, it really is only half as bad.
So a simple solution - if that is possible - is to choose narrower lenses (i.e. greater focal length) and stay away from people as much as possible. You will barely need 24mm (FF-equivalent) photos of a speaker. If you need a wider composition, be decisive and quick. If possible, make photos in fast series and then stop for a while - one click every 5 seconds is far more annoying than 20 at a time and then a pause of 15 seconds. Except from that, it seems to be the best idea to stop worrying too much and concentrate on the task at hand, which you got hired for. In my (limited) experience, it is better to not worry about slight annoyances too much. When I started my 'career', I often hesitated to get shots, just so I do not annoy people. This, of course, is a bad strategy, as you often miss chances or get suboptimal shots, which could mean more unpaid postproduction work or even the end of your career.
I am not saying "be ignorant of your surroundings", but to see it this way: You are hired to take shots, not to be quiet. I would not think that the PR department would care much if you told them "I'm sorry, I could not take the shot because I would have annoyed somebody." In fact, I know that they don't care - I worked as an intern at a local TV station once, and they got very upset with me when I delivered non-optimal clips after my first job, because the only option for better ones would have meant to block the sight of some known VIPs.
These are my rules of thumb - your mileage may vary, and perhaps some / many people may call it rubbish and directly contradict it with their experience.