@Evo very well composed question. Thanks especially for including your location. Sometimes when there are budget constraints knowing the location can help us help you find some used bargains. And thanks for describing your room. New members don't usually think to do that.
To answer your tower vs. bookshelf question, yeah, typically bookshelf speakers are the way to go. You often pay more for towers for very little to no audible benefit once you add a subwoofer and set a high pass filter on your mains.
Re: diminishing returns and tiers of improvement, yeah, home theater does seem to conform to that pattern.
Are you concerned about neighbors complaining about the noise? Is your $2500 - $3000 intended just for 5.0 channel speakers, or that + subwoofer, or all of the above + receiver? (Hint: You can probably get away with a relatively inexpensive receiver if you don't mind refurb.
Accessories4Less usually has some great deals.)
You'll typically get more for your money if you're willing to purchase Internet direct, so the best bargain might come from a speaker you won't be able to audition until it's in your home. If you're willing to take a leap of faith, then my vote is thus:
FWIW, here are
measurements of the Sierra-1s. They're pretty good, and a drastic improvement over your HTIB.
I regard ELAC as overrated. If there's a Best Buy who carries the LSiM line of Polk Audio, those might be worth a listen. Adorama has a sale on them for
$1500 for a 5.0 package. You'll still need a subwoofer and AVR.
Re: AVR being the most expensive component, I disagree. Better sound comes from better speakers, not from better electronics. You can pay $1500 for an AVR and still end up with much the same sound as you could've gotten for $400 buying a refurb from A4L. Putting more of your budget into better speakers nets you better sound.