Is Budget Audiophile an oxymoron?

Budget audiophile is no oxymoron at al! You care about sound, budget is irrelevant.

I would first sort out room acoustics. "Garage" sounds to me like cinderblocks and metal door, so very harsh sound reflections. I would first try to address any slap echos with absorption panels or heavy drapery before considering speakers. I made my own absorption panels from discarded shipping pallets, some Roxul 80 (stack of towels from good will can also work), and some breathable fabric. Very budget friendly, and easy project. A few nails/screws to hold the frames together, stapler to attach cover fabric to frame. Done.

No upgrade in speaker can fix the room. And your speakers may be perfectly fine once you fixed the room :-)

What specifically don’t you like about the sound?  Sounds like you have the speakers against the wall flanking the TV, and there are lotsa issues there that aren’t helping to say the least.  Getting a pair of decent stands and getting the speakers away from the wall and off the IKEA things alone should make a noticeable improvement (speaker placement matters A LOT), and putting a blanket or something similar over the TV when listening to music could help a bit as well.  I’d start there as it’s very cheap and will likely make for significant improvements.  

@johnmarzy Some info for you.

One primer out of many.

Lot's of inexpensive speaker stands to find

First Reflection Point ...How to find and treat

I have two pairs of B&W Rock Solids I use for TV. You can find them for around $150 a pair. Then you need a center channel and a sub, but I don't use either, I'm not really into the home theater thing, maybe when I grow up...

After 46 years in this hobby I can say 'yes' to the question.

You have what I call 'Entry Level High End', where a product family utilizes 90 percent of the technology of the ultra expensive item, but at a more acceptable price point.  Remember the 'Diminishing Law of Returns' on equipment.

Then there is (my favorite) the seller on Audiogon, (sometimes a well heeled Doctor) who is chasing Nirvana with a large checkbook.  They love to flip gently used equipment for the latest and greatest.  I bagged a wonderful Michell Gyro Table 30 years ago with SME V arm, which was 'hot rodded' up to an Orb, all only 6 months old, for the tidy sum of $3K....still in my system today!

Something else to factor into the equation is your room acoustics and your current state of hearing...You may not be able to eek out the last bit of Nirvana from that special piece of equipment....