There's a contradiction in your statement "I would like to reproduce the latest and greatest sound formats, but do not want to spend any more money for speakers". Immersive Audio is the latest sound formats and would require in ceiling speakers for optimal performance. (And you don't have to break the bank for them either.)
But I understand the desire to stay with 5.1, it's just that current 5.1 AVRs are usually just entry level these days and lack better amplifiers and features (like better Audyssey, video processing, etc., for example). Your current AVR spec'd itself at 100 W + 100 W (8 Ω, 20 Hz–20 kHz, 0.08 THD) with 2 channels driven. In those days (as was common) they didn't give anything with all channels driven but you would be happy meeting that same spec today. I suggest going for an AVR that hits your $1,000 budget.
I forgot to ask where you live as geography will impact what's available for $1,000. Also, is there a particular preference or brand you want to avoid?