Severe Singleplayer Lag in the Nether

I was fighting Zombie Pigmen in the nether and after a few minutes it became very laggy. The Zombie Pigmen started moving very slowly, "jumping" ahead a few inches every second or so.

Then I left the nether, quit Minecraft and relaunched it, opened my world again and entered the nether and the lag was not gone. I looked at a group of Zombie Pigment in the distance and thought that they were no longer angry at me, so I carefully approached them. They became aggressive and suddenly they were beating me up and I almost died if not for a potion of regeneration I had on me.

In the game output log there are many messages like this:

[Server thread/WARN]: Can't keep up! Did the system time change, or is the server overloaded? Running 51316ms behind, skipping 1026 tick(s)

I should also note that breaking blocks, picking up items and opening doors was noticeably delayed after restarting Minecraft.

I thought this might be the same bug as MC-17630 but I was not in any unreachable location after I had restarted Minecraft. (though I previously was, when I was fighting the pigmen in the beginning)

I hope this gets fixed soon because I don't want to lose my 2-year-old hardcore world to a stupid bug!