Actually, on further thinking, I think your system is internally consistent. And it's very similar to my system.
Thought experiment to demonstrate how your system works:
Virtual timeline A:
Server Violet is destroyed. I send back a message 3 days to tell myself to send inspector team 1 to prevent the destruction and tell me what happened. Sending this message invalidates the current timeline (curiously, the moment of invalidation is when the first bit is sent, do I'd better get my timing perfect).
Virtual timeline B:
I get a message from myself to send inspector team 1 to prevent the destruction and tell me what happened, and I do so. Three days later Server Violet still exists, but half the servers were destroyed and there is irreparable damage to Stored society (by quick psychohistorical analysis). I send back a message to myself to send inspector team 2, as they would be better qualified to deal with the problem. Since I never send the original message (from timeline A) and never received the message I am sending now, this timeline is also invalidated.
I get a message from myself to send inspection team 2 to deal with Server Violet, and things work out well (better than I can expect using any other team). I consider this to be good enough and choose this timeline to be final. I send back the exact same message as I received, reinforcing this timeline.
How to create an irreparable paradox using this model:
Virtual Timeline A:
Over the next two hundred years, the Mechanicans pick up the CV Sameness. It keeps the civilization from falling apart, but it also stagnates the society, destroying any potential for growth. I send back a message (three hundred years) to tell myself to prevent this. Timeline A is now invalid.
Virtual Timeline B:
I received a message a hundred years ago to prevent the Mechanicans from picking up the CV Sameness and things are going well on that front. I'm using Logician conflict to keep the Mechanicans on their toes. The Mechanican world of Wrench comes under a massive Logician metatech attack which threatens to destabilize the entire region. I send a message back a week to tell myself to tell myself to send inspection team 1 to go to Wrench and prevent this attack. Timeline B is now invalid.
Virtual Timeline C:
I still received that message a hundred years ago about the Mechanicans, and I was still using Logicians to fix it. Now I also receive a message to send inspectors to Wrench to prevent the Logician metatech attack. So, I send the inspectors to Wrench. This works well, so I send back the same message. One hundred years later I find that the Mechanicans were at no risk of picking up the CV Sameness (meaning that the resources spent on fixing the problem were waisted). This is largely because of the failed Logician attack. So I don't send back the message from timeline A, invalidating this timeline.
Virtual Timeline D:
I never received a message to remove the Mechanican CV Sameness, so I don't involve the Logicians, so there is no attack. This timeline is identical to Virtual Timeline A.
This creates a loop where we have three equally valid timelines each supporting the others. None becomes the Final Timeline. This sort of situation becomes increasingly likely as more and more temporal communication is used. Worse, it is virtually guaranteed if two or more transcendental entities are fighting.