(French fellow here)

Haaaa. It seems that the en creates many questions.

There is absolutely no problem using three en for three different things.

The only thing that matters for the en is : Will my listener understand me ? In your sentence, it is prefectly natural and I had no problem understanding you. There were no doubt about which en refers to what. The en exists to ease your sentence and frees it from repetitions.

I hope I helped you.

It is ok thanks to the context.
Remplir can only refer to the glasses. There is absolutely no confusion here.
If you used another verb that can also apply to miel, there would have been risks of confusion.

In fact, there is more risk of confusion for the first en.
If your phrase was cut at the ‘Il n’en reste plus beaucoup’. en could refer the glasses.