Converting telephone line to Ethernet

I'm trying to convert my old telephone line to Ethernet to be able to have wired internet in every room of my house. I do have WI-FI throughout the house however, I need to do this so as to pave the way in me getting rid of my cable.

My house is only 5 years old (Purchased brand new) and was already wired with CAT5e cable so it was very easy for me to add the keystone jacks to each room but here is where the problem comes in; The wiring for every room (6) is individually routed to the outside of the house bundle together with about 8" in length next to my electric meter box and cable connections.

What's the best way to make a secure and weather proof connection outside when I don't have the ability to put a punch down block on the inside of the house to make the connections. The house is completed sealed including a finished basement and I have zero access to all the wires together. Thanks for your help with this issue.