$7000 preamp vs $700 receiver - Is the difference THAT significant?

Yes, big difference.  You could go from a $700 avr to a $700 preamp and there’d be a big difference

OP, get a Mac tube pre-amp. You want blue meters, so get the blue meters. It will be a huge sonic upgrade for you and you'll have a nice piece of gear, maybe for the rest of your life. The Peachtree amp is adequate from what I read but if it was me, I might hide that amp on the bottom shelf. You will not be disappointed. 

Tube gear sounds better than Solid State. You can get Burmester SS gear and it will be very smooth and resolving and dynamic. But it will not warm your heart. 
There were excellent companies producing tube gear. THE FISHER, SCOTT, MARANTZ, SANSUI, LUXMAN ... BUT McIntosh is the only left producing it. And it was technologically leading.
I can not afford McIntosh tube gear and I am very happy with my THE FISHER tube receiver as I am into vintage tube gear.
From a vintage gear tube point of view, there is nothing more beautiful than a PRECEIVER with a magic tuning eye and a nice stereo tube power amp with 35 watts to juice it.
This leading edge gear will provide you with a very solid stereo image, muscular sound and a very high sound to noice ratio.
If you want (almost) the same level go with a 35 watt tube receiver or used "modern" (1980) tube gear from Sonic Frontiers.
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And receivers can sound really good - vintage tube receivers that is.
 

Update: I have a piece of gear inbound.  I actually made a bid on a C52, and after talking with the dealer who was re-selling it, was introduced to some other ideas.  The one I settled on, PrimaLuna EVO 400... should arrive today.  

After digging in... and seeing that SandyG himself used that equipment to demo the speakers I have (Triton 2+'s) ... I figured: "how could I go wrong?"

From all I've read, I'm sure I'll be thrilled.

Depends:  Are you running the $700 preamp into the $700 receiver?