98 Honda Civic LX has very rough start?

Sometimes will start just fine
Sometimes it will start rough, and do one of two things:
1) idle low then recover
2) die

Most of the time I have to crank it for 5-10 seconds before I can even get one of the pistons to fire, then after giving it gas and enduring violent shaking, it will be able to fire all the cylinders and start "successfully".

Here is what I have tried:
- fuel filter replaced
- spark plugs replaced
- distributor cap and rotor replaced
- used fuel injector cleaner
- changed air filter

Additional details (maybe not relevant)

- leaking water pump, has 150k miles so I'm about to change timing belt and all systems that you change with that job. Coolant leaks so I keep my res filled with water (cause it's summer).

- Oil and oil filter have been changed recently

- Thermostat changed recently as well as coolant system flushed

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