I sort of get it...
First issue, is it a solvable problem(today or with an update) to write the queue contents to disk? Preferably programmatically when the queue reaches a threshold but manually via a menu item could work.
Second issue, replaying that file to the server. This is probably not possible within Kiwi without major changes or additions. However it should be reasonably possible using a 3rd party tool such as NXlog. This would read the file and send the content to syslog. The timestamps may be off but that, for us, is less of an issue than not getting the logs at all. With NXlog we could also rate limit the sending so we don't introduce the load issue that caused this in the first place.