Well, I am not arguing whether Tidal is better or worse than Qobuz (although they do pay artists much less), just that I personally would not give them money 
PS Audio has great marketing, in person of Uncle Paul but it is mostly based on telling people interesting fairy tales
But in any case, this is just basic troubleshooting. Since whatever it is that affects drop-outs is dependent on upsampling settings, not where you get the files or how, the problem is most likely to be in the Rose, connection, or DAC (or some handshaking between them). Easiest way to find it isd to change one thing at a time. Start with the connection. If that does not change anything try a different DAC. Could be MSB, could be the cheapest $50 Topping, as long as it is known to work. If stutter goes away, you’ve found the problem.
As for I2S, the real I2S is a perfectly fine technology. The problem is that the only thing it had ever been designed for is moving data inside a device, over carefully (one hopes) designed traces on a circuit board. Between chips on that board that run off of the same system clock. There are no provisions in I2S for any kind of external connectivity. That’s why you get different manufacturers using even different connectors for it (whatever they could design in the cheapest) and even if they do use the same HDMI connector, there is no standard for pin assignment or signaling, so you end up having to fiddle with configurations, custom cables, etc. etc. to even get it to work. And once you do, you are pushing some signal that has never been designed for that, over a cable that has never been designed for that either. It might even work, but always suboptimally. And the other problem with it is that it’s synchronous – timing is in the signal, and over a length of a cable (again, that has never even been designed for that) you get some extra jitter. Generally not enough to have any adverse effect, but still. Modern DACs will usually try to reclock it properly, but sometimes it does not work.It’s basically the same as S/pDIF, just capable of doing higher resolution signal. With USB data is sent asynchronously, buffered by the DAC, and fed in based on DACs clock. Pretty much any DAC does have a clock that is good enough, and because it sits right next to it, inside the device, effective accuracy is better than from a fanciest audiophile master clock sitting somewhere and sending signal over a cable (where the clock signal also gets more jitter and stuff).
If you look at any pro equipment, or even something really high-end, you do not find I2S connectors there (with possibly an exception of some proprietary SACD player interface, and that is due to Sony’s licensing requirements; it used to be the only way to get a high-resolution signal, or DSD, without using player’s built-in DAC, was to use some hacly I2S-like connection because otherwise Sony’s lawyers would be all over you. With downloads it’s a moot point). For that matter you won’t find SPF cages there either…
I’d say you should try it both with a different connection and with a different DAC if that doesn’t help. Changing the connection is probably easier than the DAC, only one cable, so I’d start with that.