Not sure why you need to spend $300 on an ND especially at your level.
You can easily find decent ones for half that or much less. I have added a .6 ND and a .9 ND (B+W 77mm) to my bag in the last month and MAYBE spent $170 total and they are decent glass. You go Hoya or Tiffen and you should be able to get 3 or so ND filters in a variety of stops for under 200.
yes you can always change the shutter, but it does affect your shot and affect what you can and can't do. I would rather be able to keep a shutter and ISO and be able to open the aperture up. As folks have mentioned, it will reduce sharpness ever so slightly, but I also find I get less noise and better highlight and shadows with a slower shutter, higher aperture and an ND filter vs pushing the shutter extremely fast.
You are just doing video, so won't make as much as a difference, but if you start to shoot flash, the curtain and sync speed come into play and being able to keep the shutter 250 is a necessity