finding the weak link

I think your instincts are correct. If you want to make a jump in sound quality… your integrated amp is the place to look.

First question… integrated or separates. If you want to keep moving over time… then you want to go to a separate preamp and amp. Given what you have I would think upgrading to Audio Research would be the obvious next step. Either integrated or separates… Separates would be best. Alternatively Conrad Johnson… for a slightly warmer presentation… or VaC.

I also would say the Prima Luna. I, unlike others, dont like pentodes in power amps. The Hana is a good cartridge but not great. I wish I knew more about your phono preamp. Dont forget about your cables.  

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Must agree with the subs as an addition, 2 are better than 1. Your main speakers are extremely unlikely to be placed for maximum bass effectiveness, subs let you do that. I have a Vincent tube hybrid pre / power combination and use DSP to reduce the bass to the main speakers and thus demand from the tube power amp. I have severe bass room nodes and DSP removes this too. 

Add 2 REL subs. Upgrade you phono cartridge. You mind will be blown when you add 2 subs. I have a similar system to yours but with 2 subs.