Rather than quoting big parts of your post, I'm going to address the points as succinctly as possible.
I agree with others that bookshelf speakers mounted on the wall would be the best way to go. They will sound far better than your current arrangement, both because of the change in speakers but also due to the current position being awful as far as sound goes.
If it were me I would opt for a pair of Dali Oberon 1s or Q Acoustics 3010i. They're both small enough to avoid bass boom but have enough to give to ensure musical enjoyment. The Oberon 1s are less fussy than most speakers about positioning, thanks to Dali's wide dispersion design. My little JBL 52L Classics are great fun and front-ported, but they're also a bit more expensive. Either side of the fire place is definitely your best option, just leave some space between the speaker and the side of the chimney breast.
I think the question of CD playback really comes down to the size of your collection. If you only have a relatively small collection I doubt you'll miss anything with streaming as your only source. I still use CD as I have circa 4,000 discs, including some large out-of-print box sets and I'm not ready to part with them. Otherwise I would probably part with CD, keep vinyl for the physical media experience (and its analogue sound), and adopt streaming as my main source. I use it quite regularly now for exploring music, and there's a good choice of different streaming services. I use Qobuz and the new streaming platform launched by Presto Music.
The PM7000N is a very good suggestion if you want a high quality amp and streamer in one box. The HEOS platform is very good and the amplifier section will work very well with the suggested Dali speakers. It will certainly give you even better performance than a MCR-612, good though that is. If you want to add CD playback a Marantz CD6007 is a very good option. Avoid the Rotel CD11 Tribute - I have one which behaves very unpredictably and which is on its way for repair, though we all know how that goes with intermittent faults. My Dad also has one with similar faults and we're not the only people - it's a shame because it's a very fine player and I also own the matching A11 Tribute amp. My 30+ year old Sony works far more reliably and sounds every bit as good, if not better. If you don't want to spend much on a CD player and you choose carefully there's some great value to be had in buying an older player.
You asked me about my system - see below in my signature. All three sources are hugely enjoyable, and though not the most expensive I've had by any means, the speakers are the most engaging I've had. The Bluesound Node 2i streamer is very good, but definitely benefits from being digitally connected to the amp and using the Cyrus' built-in DAC. I've had much more expensive systems, going as far as QUAD Artera CD/Pre-amp and Stereo power amp with all sorts of speakers, but this set-up is much more engaging.
Hi-Fi is a rabbit warren and you can soon end up in endless cycles of swapping things around - trust me, I've been there and bought several versions of the t-shirt. Focus on musical enjoyment and easy access to your music and you'll be on to a winner.
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