Starts, runs rough (rougher at 3k-rpm) then dies. No codes

2011 Hyundai Sonata GLS - 4 cylinder GDi
engine -6 speed automatic

TLDR: car cranks and fires fine, but
runs/idles rough with low rpms (rougher at
3k- rpms) before the engine (auto trans)
"stalls" and dies with all dashlights on and
no codes indicating an engine problem.

The first problem I had with it was when I
was driving. Going 25mph in a 35zone up
hill, held the accelerator to go faster, Nothing
happened for a good 20 seconds. The rpms
didnt move, I dont think the car shifted
gears, and then all of a sudden rpms sky
rocket but he car doesnt really do the same,
so the car just dies in flight.(lights stay on,
all dash lights come on but the engine just
stops.) able to guide it safely,  next morning
it starts up fine, top off the oil (last light I
saw on, levels were lowish anyway), on the
way back from work at a light I feel the car
have little to no power. I start to pull over
and sure enough, rpms jump, engine dies,  
all dash lights turn on. I pull the codes, only
one that shows is a "driver door ajar", was
able to drive the car to a shop with a battery
charger hooked up. I get the it cheshed by
the mechanic, they find NOTHING wrong,
they say took it on drive tests with no
problems on the highway. (Said IF anything
a. faulty fuel injector - pays $65 for a
professional to say "I dont know") drive it for
2 days, check engine light comes on, take it
to a different mechanic they pull codes, "the
crank shaft sensor is bad", they say if
anything could be the timing belt and water
pump (pretty sure the car has a timing chain
not belt) gladly paid $65 cause they actually
did something. Next morning, start the car,
cranks -fires - starts like normal. Let it sit for
Approx. 2 minutes just and case and ...
Rpms drop, idles rough, engine cuts as if it
stalled, light stay on and all dashlights turn
on. No check engine light though, even
though it clearly sounds like the engine.