Have you done any stress testing to check thermals?
I'm currently running the asus z370-i mobo with an nh-L12s and considering upgrading to the z390 itx phantom + shuriken fan that you have. knowing the sort of thermal performance to expect and at what frequencies/voltages you are running would be super helpful!
Sorry if this comes too late, I hope this information is still helpful, and I'd love to know how your setup fares comparing to mine.
I did some simple and not-so-rigorous testing with the two coolers I had in hand - I got the new Big Shuriken 3 as soon as it's available in my region - with my 8700k and ASRock Z390. I'll start with comparing the two coolers, then try to answer your questions regarding thermals. In short, the new Scythe low profile cooler has excellent compatibility and will fit with almost all Z390 ITX boards with the stock fan (and so it fits within the LZ7), while allowing unlimited RAM clearance. However, the build quality is pretty poor comparing to the L12S (mine had several heatsink fins slightly bent out of the box), and it is struggling to keep up with the L12S' performance even with the latter having a 12mm slim Scythe fan in my tests.
I had my 8700k @4.7GHz all core at 1.23v running AIDA64 AVX (hitting 95+ pretty quick for both coolers), non-AVX (85 degree for 5min for the Noctua with a slim fan, slightly higher for the Shuriken), and Cinebench R20 (didn't record any data lol), with chassis fan hooked up with CPU temp and all fans running on performance mode (around 1700 RPM under gaming load for the Shuriken's 15mm fan and the L12S' 12mm slim fan, 1200 RPM for the chassis fan). No matter the chassis/cooler fan configurations - I tried all the combinations I could think of with both coolers in terms of pushing/pulling - the L12S did ever slightly better or about the same as the Shuriken in all the tests.
This is surprising as many other reviews have shown the new Shuriken to be at least comparable to the L12S. Of course, considering how poorly I controlled my variables, it might very well be a problem with my testing method instead of the cooler. Other than this, my totally uneducated guess is that the new Shuriken is so low-profile it blocks the lateral airflow (see pictures above). Anyways, you should expect pretty good thermal performance with the L12S even with a slim fan, the only problem being the slim fan can run pretty loud under load. The actual thermal performance would of course depend on how much you overclock it and how good your CPU is, but 4.7GHz or even 4.8GHz (if you can somehow fit the NF-A12x15 in) should be totally fine for daily use.
Now comes the dumb part - I'm sure you have enough common sense to NOT try this yourself - I managed to snap off the heatpipe that connects the two-part VRM heatsink, and only putting back the part over the m.2 slot (which is necessary if you want to install the m.2 drive at all). I can now install the L12S with the stock fan, and the thermals are now superb. I was running the 8700k stable all core 4.8GHz at only 1.18v ('Lucky me!', I thought too soon, see below), and it never runs past 57 degree even during extended gaming sessions, averaging at only 55 most of the time. I was able to past extended stress tests and benchmarks with this voltage/clock combination, and also a slight OC on my 16G Vengeance LPX from 3200 to 3333 @1.35V, same timings.
That is, until I shorted my motherboard, CPU and PSU by wiring the power button wrong (yes, this was my first ever PC build). I'm pretty sure it has nothing to do with me breaking the VRM heatsink... Or am I? It definitely had nothing to do with undervolting. Putting this aside, the L12S provides excellent cooling for even an 8700k inside the LZ7, and for more powerful CPUs I'd pick it over the new Shuriken even with compatibility issues and the slight price premium.
A harder to implement but probably the best alternative is, as
@K888D suggested, to sand 2mm off the VRM heatsink on the ASRock board if you have the tools. A simpler alternative is to get the Gigabyte Z390 I Aorus Pro Wifi instead (which is what I got to replace the ASRock I killed), which AFAIK is the only 'good' Z390 itx board with VRM heatsinks low enough to allow the stock L12S. I'm not doing any heavy overclocking or extensive tweaking so the difference in daily use comparing to the ASRock is minimal to me (other than the fact that the Gigabyte bios is horrendous).
As a side note, I tried out GPU undervolting after seeing what Optimum Tech's done with his 2080Ti (also mentioned by
@K888D). In short, it's absolutely worth it: my Gigabyte 2070 mini now runs 1920Mhz at 0.9v (dropping down to 1905MHz above 60 degree; or it can run 1890MHz at only 0.881v, but the temp/noise reduction I got from further reducing voltage and clock speed is diminishing after this point), and my GPU peak at 66 degree in Heaven and hover around 61 degree when gaming - a ~5 degree drop from the stock settings (@1.125v 1905MHz boost). I'd highly recommend people with a mini card to try this out.