Is this normal behavior for a 4 Mhz zip chip?
No, that's definitely out of the ordinary.
The only 'odd' behavior I usually have to warn people about is when turning off a ZIP-equipped machine, they wait for the power to bleed off before turning it back on so the cache is flushed (especially with 8MHz ZIPs).
Did you check the ZIP's config with the ZIPCHIP Utils for anything borked? Does it pass diags?
Yeah, that's one of the first things I did. Everything is ok now.