Have rarely had a problem upgrading to J from K with miles, until my last trip, when they made me pay £126 to upgrade to W (I think) first. Then I could upgrade - maybe they are clamping down. I don't know if I was lucky in the past - I think there used to be a policy of allowing this on the day of travel if there was space. Maybe that has changed?
I always do my upgrades at the airport, and had very friendly service in doing so. Just be polite and ask nicely - it goes a long way. From my experience - if you intend to do an upgrade like this, don't do a DIY check in to your allocated/chosen PE seat. It may mean you need to be offloaded from the flight then re-booked before they can upgrade you. That can take a while! And the earlier you get to the airport, the more likely you will be to find a UC seat available for upgrade (and the longer you can spend in the Clubhouse

).
Andrew