You are a smart momma to not put a 3-year-old in a booster seat. Those are best for ages 6 and up. How about the Evenflo Maestro? It has one of the highest top slots on the market (18") and is under $70 or $80 usually. It only goes to 50 lbs., but it sounds like she is light. The carseat is light. Easy to install with seatbelt! Or you can use latch to its limit, but I find seatbelt easier.
My toddler's carseat (Orbit toddler) DID cost $600 exactly, actually (with the base), so I hear you on wanting a seat that doesn't break the bank! But it saved my back since it rotates for rear-facing.
My kids are VERY tall and all have been able to rear-face in the Diono carseat until age 4 or 5. Now, those are over $200 too and heavy, so they stay put in the car. Top-notch safety with extended rear-facing, but I am sure the Maestro would meet your needs. If you want the seat with a higher weight limit, try Evenflo Secure-kid. It's affordable too.
If the straps are below her shoulders, I would recommend getting the new seat today! Good luck!