I get a very similar issue, and sometimes that 'Attempting to reconnect' box appears, I lose control of my character and I can't even use chat, I'm either stuck in spot for long periods of time (up to 15 seconds!), or running uncontrollably towards whatever attack target I have. I can still level up my skills, but I can't use them. My ping remains constant, and my FPS often remains at 60, but I noticed a drop to 30 once during a freeze. It makes the game unplayable, and I hope these issues get fixed as soon as possible.
To clarify further, as the OP mentioned, all other champions and minions behave normally, it's just my character that becomes inactive and only auto attacks. There are no catch-ups, gliding, or strange behavior. I simply can't control my character, and it leaves me helpless against any attacks.