@boneius - Welcome to AudiogoN forums!
So, you're asking about your vinyl rig and looking for potential upgrades. And the MMF-7.3 suggested by @sonicjoy
is certainly a viable option. However, you also asked:
Is there something else in my system that might be a weaker link.
Looking at your setup, I would think the Cambridge Audio Azur 651R AV Receiver might be the weakest link. Admittedly, I have not heard that particular model, so I'm simply basing this opinion on my experience with AV receivers in general. AV/HT receivers have a lot of features built-in. Many of these features are geared toward video functionality and HT codecs, not music sound quality. So my question would be this: Do you need all of that functionality that an AV/HT receiver provides, features such as 7 channels of amplification, video switching, HDMI inputs, digital format decoding, am/fm stereo tuner, etc.? If not, you might get a bigger boost in sound quality by upgrading the AV receiver to a quality Integrated amplifier. You will lose the tuner, all of the video switching , extra channels of amplification and HT digital inputs. However, you would likely get better 2-channel sound quality.
Sorry if I went off subject a bit. But I think it might be a better first upgrade. That is, if you don't need the AV/HT functionality that is built into your current receiver. If you do need/want the HT funtionality, proceed with the TT upgrade.