I just removed the front sprocket cover and discovered that there are chunks and chunks of nasty goey/gum/oily crap stuck to it. Not sure if it's oil that's been there for too long? chain cleaning crap? anyway, I had to scrape it all off with a screwdriver and it feels like scraping off gum...
Can I take the wheels off and clean/do everything you suggested without cutting the chain? I want to hold off on replacing the chain and sprocket for now due to cost concern. Also, for the life of me I can't get this bike on its centerstand, is it just me being 130lbs or is it really tricky because it's not an OEM part?
One thing to be concerned about is getting all the goop on the tires. This can be direct or after you're done and it' flicks onto the tire.
You don't really need to remove the tire to do a good cleaning. Spray cleaners, parts brushes, etc, can do a great job.
being dirty doesn't damage things, it's when it where the chain is. So all that goop isn't really a problem if it's not getting onto the chain.
I'd start with a good cleaning and checking of the chain, clean, oil, adjust. The dirty parts can be cleaned, but remember to keep it off the chain. A handful of good rags and cleaner can go a long way.
What advantage is there to removing the tire and doing a full cleaning, maybe wait till you do the chain replacement.
There's a nice kit being sold here, it's < $200 IIRC.