If I'm understanding this correctly, you only have an LED at the base of the blade, and no lights going down the length of the blade? The tutorial uses an LED strip that runs down the entire length of the blade, but it sounds like you just put lights at the very base. Just wanting to make sure I have that right.
If that's the case, you are going to be hard pressed to get the entire blade to light up when it is that long, unfortunately. LED strips can be mega bright, and the strip is putting bulbs in the blade all the way down to the tip, which is why the tutorial blade is so bright, even with lights on.
My friend recently made a light up sword for her Rin Okumura cosplay. She based her designed off of that same tutorial, but made some modifications. She used a blue LED strip and ran it along the spine. It is blindingly bright on its own. Then, to get the light to spread out and look even down the blade, she took a high grit sanding block and frosted the plastic. This made it half opaque, but it was still see-through enough for light to break through, but at the same time, dispersed the light. The LED strip was bright enough that the half opacity did not obstruct the light much. She then hand painted on some silver acrylic so that it would be a silver blade with the lights off, and that went on pretty transparent. When the lights are on, you can't see the paint at all (no brush strokes even - lights are too bright!).
Before she went the frosting + acrylic paint route, she tried silver spray paint on a scrap piece of plastic. She got the same results as you, with the blotchy unevenness in the thickness of the paint, and the light of the LED strip would only really show through on the areas that had only speckles of spray paint. I have no idea what spray paint the person in the tutorial could have used to avoid this. That spray paint made my friend's scrap plastic instantly opaque.
Given your time constraints and the fact that you don't have the LED strip set up, I honestly think you will be better off with moving forward with your sword not lighting up and just making the paint job look nice. I don't know the right way to remote spray paint from something like clear plastic, but a few years ago, I sprayed on some Krylon clear varnish (meant for acrylics) and something about the chemistry of that with the thing I spray painted caused the spray paint to come completely off...I still don't entirely understand that, but you might be able to try that if you really are set on trying to remove the spray paint? Otherwise, if you try to sand it off (with high grit sand paper), you will end up scratching up the plastic. This is fine if you wanted to try frosting the plastic though.
But yeah, I honestly think you are better off just making your sword look good as it is right now, and making a new one with the LED strip for a later convention. I just don't know how you're going to get the whole blade light up like you want with LEDs only in the base.