How to transfer signed tx from coldstorage to online system for submission into blockchain?
I would reroute all incoming deposits to cold storage, which I would keep in small portions on different addresses. 

Then I'd import some cold storage addresses to my hot wallet whenever my hot wallet is running low, keeping the amount in my hot wallet in the range between "not empty" and "what I'm comfortable having in the hot wallet".

As Mike mentioned, multi-signature addresses could provide additional security, and accountability.