PIC chips are extremely tough little buggers.

Here in Colorado Springs the humidity hangs around 10% most of the time.
We'll draw 1/8" to 1/4" arcs when you touch anything, even if it's not grounded.
You can draw an arc touching a wood door. I've never seen anywhere quite like it.

I do not use any kind of static wrist bands or mats.
We have several hundred different PIC's in the office, and to my knowledge not a one has been toasted by a static discharge.

If we're passing a circuit board between two people, we'll set it down on a table and let the other person pick it up.
But that's mainly because person to person arcs are huge.
The PCB is likely to go flying just from your arm jerking away from the pain. But the chip will be fine.

So I'd look at other possibilities before buying a bunch of anti-static equipment.

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For the bad address error, ... programmers don't look at the chip to see if an EEPROM address is valid or not.
They look up the address ranges from a database or parameter file.
If the EEPROM wasn't working, you would most likely get a Verify Error instead.

And the 877A's don't sound like dead chips either, but it's hard to tell without more information.

What programmer are you using?
What are the configs set to?