My Oxford Hachette French Dictionary only lists one r sound, namely R. Where does the upside down R occur? Curiously Wikipedia, which is often unreliable, uses only the upside down symbol to represent the French r sound.
On reading your post several times, I am confused. Are you struggling with R or the upside down R?
It seems to me that there are variations of the r sound depending on the speaker. It can be very light, with very little motion of the dangly bit, or it can be very strong, with the dangly bit flying all over the place, putting the listener in fear of large globs of flying spittle. My impression is that speakers who wish to sound posh or correct use the stronger form, but I don’t know if that is a correct impression.
I’m sure you’ve seen many YouTube tutorials. I will add a few comments in the hope that they are of use.
Speakers of English and other stress timed languages can struggle with the R sound if they use English timing i.e. stress timing. I don’t know if this applies to you, as I don’t know your L1, but make sure you are using syllabic timing in French i.e. you pronounce each syllable clearly and with roughly equal weight.
When I speak French, it feels as if I’m speaking from further back in the mouth compared to English. To pronounce a French R you need good control of the back of the tongue, which only comes with a lot of practice. You are having to create new muscle memory, which means doing it slowly at first, then practicing with easy words, such as rang, and moving on to harder ones such as arriverai and rentrerai. In other words you have to go through a process of training your mouth, and this should be done outside of actual speaking. In essence all you are doing is exhaling while tightening the throat to constrict the air flow so that it sets the dangly bit in motion. For what it’s worth, it took me months of practice before I was able to vibrate the dangly bit, and lots more months to develop finer control. I saw a big gap between being able to make the sound, and being able to use it naturally in speech. If you listen to babies, you will notice that they make a lot of weird sounds before they start speaking, and probably after too. They are of course practising making the sounds in their L1. And they spend a lot of time doing this.
Learning to pronounce foreign syllables takes a lot of listening, so you know how they should sound, and a lot of practicing.
Apologies if the above is obvious.