Regarding the log,
I have never performed a Strongman comp, nor trained the implements, but a few weeks ago I was at my girlfriend's gym and found, of all things, a Strongman log sitting in the corner. Labeled 145 pounds, for what that's worth. I was able to push-press it about as easily as I can press a 145-pound barbell. When push-pressing the log, you get a little extra from the bottom because it's resting on your chest so as you start the upward drive, so the pressure of your chest starts moving the log upwards (and the diameter means you're starting a little bit higher than you are with a barbell).
EDIT: I just re-read your post. If you can push-press 90 kg, you can absolutely get an 80 kg log overhead. I will note, however, that cleaning the log is VERY odd if you're not used to it. It is nothing like a barbell clean. Unless you're strong enough to just rip it from the ground straight up to your chest, you will have to haul it up to mid-thigh, pause, then sort of roll it up your front-side. I posted a video in my training log of me pressing the....well, log...if you want to see what it looks like when a beginner to the implement tries it.
So I might err on the side of the 70 kg log just to make sure you can clean it, haha. You might knock off a decent number of reps, too.