I just replaced mine for the second time two weeks ago... It is a tight squeeze getting the fuel pump out with those plastic tabs on the side of the fuel pump.
I lifted mine out at a slight angle until I could get one side of the fuel pumps plastic tabs to sit against the fuel tank neck. I then pressed those tabs against the neck firmly and then slowly straightened the fuel pump and was able to pull it out very slowly.
I also used a manual gas can pump, to get the remaining fuel out of the fuel tank to be able to remove the debris that was floating around the bottom of the tank. I would spend a little extra time removing said debris as this should extend the life of your new fuel pump.
Make sure that you also replace that green seal as it can get gummy if/when fuel touches it. My new fuel pump did come with a new seal, some do not though.
Edit:
@2001ZR2 The fuel pump (for sure) and I think the tank were both changed in newer models. MAYO3LT has the older style pump in that video.
Your pump has the plastic tabs in the middle of the fuel pump like mine does. Circled in the screenshot below.