No decoupling wont help.
Yo u can use a speed up feedback capacitor from output to input (100pf )?
I have used this comparator in a LC meter and it worked up to 100KHZ fine.
Your waveform looks like the scope is on AC setting when it should be on DC.
One thing that hit but might not be a problem is your lower comparator input goes to ground which means other input has to go below zero which might latch it up. Might work or as is.
A slow moving input definitely needs hysteresis with a speed up capacitor.
Also any comparators I have used need pull ups on the output.