If you can simply connect the external HDDs to the Cambridge Audio and you are satisfied with the quality then nothing like it. Just put aside everything and enjoy the music and movies.
However if you are decided on an upgrade path, before you do anything else buy a Raspberry Pi (Rs. 2600), a microSD card (Rs. 350), and a power adapter (Rs. 500 or you can use any mobile charger), spend a day learning how to write the OS to the card, set things up, install moOde Audio Player, and wirelessly stream music to your AVR. You will need to plug in your external HDD (containing the music rips) to the Raspberry Pi.
It is important you don't use any cable to connect the Raspberry Pi to the Cambridge Audio receiver. You don't want to be using the internal DAC of the Pi. So use wireless streaming, its available in moOde. You can use the excellent BubbleUPnP with any Android device that you have, or find something similar for iOS.
Just let the music play and see how much of an improvement is there over the previous source/transport. Everyone of us has seen immediate gains, though they may be subtle, and take time to process and observe. If it works, excellent gains for Rs. 3000-3500, and if it does not, then you have not lost much, and you can go back to using the Raspberry Pi for video streaming or even live streaming of TV channels.
Next goal will be ramping things up...
I have tried all "connections" from HDMI, USB, Coaxial, Toslink, wireless, and even ethernet. I have a friend for whom ethernet works really well, while in my case the ROI has been excellent with Toslink.
Everything has its own advantages as well as disadvantages, find what works for you and do the best with it. However, ensure that you spend the most on the equipment and not the fixes. I have seen folks spending more on USB cleaners and linear power supplies, even to the tune of over $1500, while a DAC in that price range would do so much better than the sum of all parts. Don't fall into that trap, where you will need a "fixer", and then a "fixer" to fix the "fixer".
If wireless via the Pi is working well then let it be. Enjoy the music and work on the DACs later on. For now let the improvement be in the areas of source and transport.
Some of the best improvements I have heard have come from going wireless (and in part from isolation). I have heard setups where the source was completely eliminated from the rest of the chain, either with the use of a NAS or a music streamer. In every instance, the gains were immediately apparent and also quite huge with some of the equipment. For this part of the improvement process, we will be focusing on the external HDD connected to the Raspberry Pi. The goal is to set up a proper NAS, a DLNA server, or a media streamer, or a little bit of everything. The easiest path here is to go with something like Synology. The advantage is to add multiple devices later on and stream to different rooms of the house from a common centralized NAS.
Of note, the NAS will also let you stream content (wirelessly) to your Cambridge Audio AVR. In fact, you can dispense with the Raspberry Pi at this point. However, IMHO you should continue using the Raspberry Pi, with a Linux distro like moOde because it makes a huge difference in sound quality.
Instead of a NAS, you can also go for a media streamer (some of the expensive toys you were referring to earlier), but ensure they are wireless capable, run preferably on an SSD, and have a large amount of storage. Obviously, such streamers are easier to set up than a combo of a NAS + Raspberry Pi, however some of them are also exorbitantly priced. I believe you will be better served in the long run by learning to tinker and set things up yourself, and it is also very easy to update/upgrade parts of the chain instead of a single expensive unit at a later time (you run out of space, it is much easier to add HDDs to the NAS, or throw in a more powerful Raspberry Pi, etc.). I saw a 12 TB media server for nearly $18,000, and all it did was play CD quality content, no DSD or upscaling. Hard to replace or upgrade and that's the kind of problems you will run into with media servers and streamers.
After the source and the transport, next path of upgrade should be the AVR and/or DAC. A couple of points you should note, when buying an AVR you are not paying for the DAC, but the amp in the AVR. In fact most of the DACs are a single chip solution and they are available in all devices from $20 soundcards to most mid hi-fi equipment. In other words, a 50W $100 AVR most likely will have the same DAC as a $500 AVR to even a 200W $1000 AVR. The price difference is only because of the amp and not the DAC.
Even more interestingly, if you are sending audio from the same file, or even lossless music then all DACs should sound exactly the same. Any changes will be because of the processing involved in converting digital into analog. When a DAC starts changing the output it means only one thing, the sound engineering is using EQ settings that are coloring the sound. This is not a bad thing, some people like the sound signature of certain companies, but not everybody does.
So in theory, you are actually paying for sound coloration that you like, or you can pick up a $60 to $150 DAC from the likes of Schiit or SMSL and simply be done with it. Needless to say, you will find the most varied opinions in this area as well as the most passionate people who will swear by their choice of sound coloration. You can continue to use the AVR with the addition of a DAC, or you can also look at adding an amplifier for music. I use both, an integrated amp for the main rig, and an Onkyo AVR for the bedroom.
Just to sum it all up:
1. Don't buy anything just yet.
2. Start small with something like the Raspberry Pi.
3. Work on improving the source/transport.
4. Finally, focus on a DAC and/or an amp.