ReplayMod 2.1.4 on MC 1.12.2 should be working with Optifine E1+, so that should be fine.
Unfortunately your log doesn't contain any crashes. It just looks like starting Minecraft and then closing it again. To make sure you get the right log:
1. Clear the logs folder
2. Start MC
3. Get it to crash
4. Check logs folder
If I had to take a guess, I'd suspect TickRateChanger (iirc there were unresolved issues with it before) or ServerTabInfo (seems like something which could break when in a replay) the other mods SEEM unlikely to cause the issue.
As for the Java version: Both, you and OpenEye, are right. While you do have the latest Java version installed, Mojang at some point decided it'll be easier to package their own (by now horribly old) Java version with the new launcher and that's the Java which is actually getting used by Minecraft.
There's nothing you can really do about it (well, technically there is but it's not really worth doing).
So, unless you have issues with Java itself crashing, you can safely ignore OpenEye's warning.