I don't think you're understanding, no manager leaves on good terms when he's sacked in private anyway, but in public, it played out quite smoothly once he was sacked, Levy stayed silent and Redknapp did by his standards. There's always ways you can have a dig at the club that have just fired you without it being libellous. Pretty sure Ramos had a few sly digs at us within the last year or so.
Sorry but I just don't buy that he was looking to get sacked. Once the England job was off the table, he was never going to get a more high profile job than Spurs without some incredible luck, certainly not in this country. Your theory might make sense if you could name a credible job offering that was on the table waiting for him.
I don't really know how to answer your last question, by the way you asked it, it's clear you want me to agree with you but maybe he thought two 4th place finishes would be enough to deserve a contract extension.
Why don'y YOU answer ME one question, name a bigger club that he could have become manager of? I know Chelsea were linked with him but they had just won the CL so they weren't going to get rid of Di Matteo in the summer, Emirates Marketing Project had just won the title, Fergie and Wenger were both still around. That just leaves Liverpool and I can't believe he would make the trip from the South coast to Liverpool every other day at his age.