The network never "choked" at 1.3tps. There are peaks of activity near the theoretical max of 7 tps (check for blocks close to 1MB in size). There are thousands of unconfirmed transactions because their senders chose to include fees that are too low (or no fee at all), so miners decide to not process them.

> When new coins are no longer being awarded to miners then people will have to start to pay the transaction fees themselves

That's not how it works. People (senders) already pay the transaction fees themselves.