Before death:

After respawning:

This was observed with only Forge 10.13.4.1614 and Ears1.4.1 installed.

Of interest: Installing bspkrsCore, which adds a renderer to the main menu of the player and a random mob, seems to also display this behavior somewhat. Ater loading up the game for the first time, the player renders correctly on the menu:

But after navigating away from the title screen and back, it's broken now:

This leads me to believe that the issue only occurs when the player model is completely re-rendered, like when the player respawns or in situations like the model being rendered on the main menu.

1.7 is a really awkward version as it's before the 1.8 player model changes but after the API rework; will look at this

I have to wonder if it'd be better to just treat 1.7 as a vlegacy version and ignore its janky partial implementation of the new skin system...