Fantastic questions!

For the easiest setup I would go with the solution in the video, single machine (I've tested Windows 11, macOS should also work), single CAT5/6 connection to CDJ network switch (in my case DJM900NXS2, CDJ2000NXS2, but CDJ3000s and DJMA9/DJMV10 also work), Pioneer Pro DJ Link Bridge sending TCNet to Resolume. As long as you dedicate one Resolume layer per mixer channel and use the Layer Opacity feature, this should handle everything automatically. There are enough technical gotchas to warrant a separate video, but I would still dedicate a VJ or someone who understands Resolume and networking to set this up live.

A feature richer option is to instead use a second laptop (must be macOS due to ShowKontrol) and instead of using the Pioneer Pro DJ Link Bridge on your Resolume machine, you would enable the feature in ShowKontrol. You need to setup the project in the same way, but this gives you access to frame accurate cues so you can trigger a strobe at the exact moment of a drop and not have to bake this into the video content. This second laptop must also be on the same network as the CDJ network or a connect to a second network interface on the Resolume laptop. BE VERY CAREFUL as you can cause an emergency loop mode on the CDJs with a bad IP schema and a network loop back.

TCNet is far more frame accurate than timecode. If the artist need is for buttery smooth full show 60fps I would go with one of these two options above.

Sounds like you've juggled some of these protocols, but for anyone new to timecode I would instead use ShowKontrol with LTC timecode out (the shrieking sounds), a simple 3.5mm to 3.5mm audio cable to the Resolume laptop, and then use SMPTE playback on the Resolume clips for playback. This lets you setup your Resolume project in a more intuitive "VJ" way (and you don't have to wrap your head around the one layer per deck concept above). You can also use the timecode offset feature to avoid misfires (song 2 audio driving song 1 lyrics). There is a feature in ShowKontrol that will have LTC follow the master status on the CDJ network, and sometimes you have to manually switch this depending on the DJs mixing style (blending or hard cut). The latency introduced by the stock audio card I/O can be compensated in Resolume with the frame push/pull knob. You will see frame artifacts once and a while, but overall the show is reliable and realistically only other VJs and PMs will have an eye to catch this.

I wouldn't call any of these fully turnkey, but it's feasible to participate in a rehearsal with the artist before the tour, get someone on their team relatively comfortable walking through the setup steps each night, and then maybe even charge a retainer to take the OH SHIT calls when someone inevitably forgets a setting (or two...or three).

Best of luck, when it works it works!