To do analysis on the merits, you have to look at why the “authorities” came to the conclusions they did and start showing how they may have been wrong. Science isn’t an authority game, it’s an evidence game; you need to start by looking at the finest details available for both this beastie and the others of its time period. Which means going to the experts at least long enough to get that data.
I’ve been trying to find the Steven Jay Gould quote on Hallucigenia where he apologized for, like everyone else, having misinterpreted it by holding it upside down. It amounted to “when that’s corrected, this is a very standard body plan for this group, and I’m embarrassed not to have seen that immediately.” I admit that tends to make me skeptical about trying to declare another reinterpretation on the basis of spines (which have independently evolved many times) and what you’re interpreting as tube feet (which needs more investigation and which even if so might be a parallel evolution).
Certainly I don’t see the radial symmetry which the echinoderm body plan generally shows; that’s one obvious point you’d need an answer to. It’s possible that’s an artifact of the the beast having been pressed into a single plane during fossilization, but …
All we can do here, unless there’s an expert involved, is raise questions that you’ll have to resolve. To resolve them you need to start digging. If you want it to be taken seriously, it’s up to you to start by taking it seriously. Most scientists are delighted when someone shows interest in their work. They aren’t hard to find; hit a college with a paleontology department (preferably one which has a history of publishing on the Burgess shale critters so they’re more likely to have have direct access to specimens), or a natural history museum with a paleontology research department (I’d suggest the American Museum of Natural History), and ask them “Hey, has anyone considered… and if not, why not?” If you approach it that way, rather than asserting that you Have The Solution, odds are that you’ll get expert assistance in understanding what it would take to defend or refute the idea, and if you’ve really got something worth investigating you should be able to find someone to help you take it forward.
Scientists are usually delighted when they can say “oh, that’s interesting, we didn’t consider that and it’s plausible.” But first you need to get involved in making it plausible.
If you’re serious, you’ve got a direction to go. I’m sorry I don’t have a specific individual to point you to, but you really shouldn’t have trouble finding one or two; start by firing off some letters to department heads. Meanwhile, hitting libraries which carry the field’s journals to see what’s been said in the past shouldn’t be hard and, if you’re interested in the field, might actually be a lot of fun. Hitting the high-level popularizations like Scientific American might be an easier entry, though you’ll probably have to go beyond that.
Have fun.
