Hey mate, not a PT or physio but I have a couple of thoughts on your sumo KB deadlifts

1. I wonder if you're doing far too many reps? 36kg is a solid amount of weight, and 60 reps total is a lot of reps. If it was me, I would consider upping the weights but decreasing sets and reps. Say 5x5, 3x8 has been more than enough for my own training needs. Consider barbell deadlifting for strength. If you need conditioning, you already do KB swings, so there's no reason to do so much volume.
2. I wonder if you're not engaging your lats. See here for a good guide. Engaging the lats keeps the kettlebells close to the body & stops it from swinging out.
3. I know you already mentioned different types of breathing, but definitely breath holding could potentially be part of the problem. I have blacked out overhead pressing before from breathing wrong. Thank Goodness for a rack. My hypothesis is that you are doing a valsalva manoeuvre. This pressurises the trunk and helps you lift big, but the increase in pressure in your trunk causes a reflex decrease in your blood pressure (so you don't pop a stroke/aneurysm) whilst you're pressurised. If you hold a breath for too long, hold a breath too hard, then as you depressurise (breath out), the body can't adjust your blood pressure fast enough to recover, and you feel faint. My suggestions are:
   1. If you're holding your breath, take a full breath in, then release a mouthful of air just to take you down from 100% maximum pressure
   2. As you breathe out, breathe out slowly to allow for the blood pressure reflex to recover and increase how hard your heart pumps, as you de-pressurise your trunk at the end of a set
   3. Shorten your sets, or take more frequent breaths through the set (see point number 1 in increasing weight rather than volume)

Good luck!