I would guess that 1000 log requests per request is highly significant. Your best bet is to adjust your log level, maybe up to warning or error, deploy and see if there is any noticeable change.
You haven't quantified how often you get Deadline Exceeded, so it will be hard for anyone else to answer your question. Apart from instability with internal services, exceeding deadline is an issue with the code you deploy. Appengine has generally been getting more stable over the last few months, and now issues are detected and generally sent around on the notification group in a much more proactive fashion.
If you are getting this at a level that is driving you to distraction, then it is either:
a) caused by you
b) caused by data centre configuration that you suffer more than others (such as networking configuration to a particular geo location or unusual use of a service)
You can try making quantifiable change to resolve (a)
You can raise a support ticket to resolve (b) - if you have support.