[Zope] Scaling problems, or something else?

[Gaute Amundsen]

Just a quick call for ideas on this problem we have...

Setup: 
Zope 2.7.5 (~180 sites) -> apache (-> varnish for 1 high profile site)

Most noticeable symtoms: 
Takes 30 sec. or more to serve a page, or times out.
Sporadic problem, but allways during general high load.
Lasts less than 1 hour. 
Restarting zope does not help.
Lots of apache processes in '..reading..' state
Apache accesses and volume is down.
Server load is unchanged, and < 2.0
Apache processes is way up (~250 aganinst <40)
Netstat "established" connections is WAY up (~650 aganist < 50)

Is this zope hitting some sort of limit and just letting Apache hang? 
Would setting up ZEO on the same box make a difference, or would it be better 
to extend varnish coverage?

What would you do to pinpoint the problem?

Any ideas are welcome!

Regards

Gaute Amundsen