Well, firstly, if the problem is really a timeout (ie you get logged out when trying to send it all) then you need to increase the allowed session time, see admin >> configuration >> variables. Make it as much as you like.
As to the overwriting when several teachers are marking at once, I remember that this was addressed in the Assignment at least, but I don't think anything special was done in the (soon-to-be-defunct) Journal. It is possible to overwrite each other's feedback, so either save often or split up the work somehow so you don't tread on each other (you could put the students in groups, for example).
Journal (plugin)
Problem with responses to students
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