Sorry I couldn't see the images you posted. Basically it sounds as though you have played primarily FR games previously. 6 max tables are very different as you have seen. The play is far looser over all and they seem to attract less experienced players in my opinion. What should you be playing? I think the answer is staring you in the face. Which tables have been more profitable for you?
You made a comment,
“Now a raise preflop in FR usually signifies something so if it's a big raise and I had a middle pair I'd fold”
You would fold 99 to a “min button raise” while in the BB? I hope not! What I mean by this is that 6 max games are like real estate, “location, location, location”. Well, position, position, position! I think everything at these tables are magnified. That's why it's easier to catch the weaker players because what may be a small mistake at a FR game is huge at 6 max.
In a nutshell play solid poker. Pay attention to position. Use a heads up program that will help target the loose aggressive players. But don't play the stats! If a player has VPIP 90 and PFR of 80 NEVER assume they have nothing! Those stats just tell you they are less likely to have a hand preflop.
Swings. Yes the swings are larger here. I think the key to controlling them is to not get involved in a lot of huge pots. The weak players are attracted to the large pots and a quick return. It's not uncommon to see a player shove with a medium flush draw with a small pot. Why risk your entire stack to win the blinds? It makes no sense. Why risk your entire stack calling a donk with middle or top pair when you can chip away at their stack chunk by chunk easily with minimal risk? Try and avoid calling allin raises with less than the 3rd nuts or better. That alone will reduce the down swings in your game.
Fold kings preflop or not? Usually no. But it all depends on what happened ahead of you, how they have been playing and go with your gut (a lot to be said for that and had you done it you would not have lost $10)! I've laid down KK many times preflop at 6 max. Example, 2 donks shove all in PF, 2 other players that have played very few hands and always flip over the nuts call. It is a pretty good bet one of those tight players have AA, KK or AK. Why risk your stack when the odds
of being beat are that high? I prefer to win a lot of smaller pots than one big one. You may win that one but the next most likely won't turn out as well. A good player shouldn't need to gamble!
EDIT: Now I can see your stats. Wow you play a tight passive game! Loosen up a little, within reason. Try something as basic as raising with any ace on the button. Use that tight image to your advantage! Semi bluff more often. Don't go crazy with bluffing
though. Regular stone cold bluffs at micro is a losing proposition! But you do need to open up your game more for 6 max.