Upgrade: will I hear it?

Been thinking about adding a true preamp and or upgrade DAC. Need advice.  Budget $2-3K. Current system is a Cambridge 851N into a Marantz AV8802a pre/pro to Bel Canto Ref 500m monoblocks to Dali Mentor 6s.  
I use the Marantz as a preamp. Before it I used an 8801. 
I listen to Qobuz and ripped files.  Jazz and Classical. I also run SACD DSD they HDMI through the Marantz and also TV sound. 

The 8802 was a big upgrade in two channel sound, and the advanced Audessey room correction really helped—in my old house. But we moved.  Listening room is now very big, speakers out from the walls and room correction not needed as much.   I’ve used the Cambridge (digital) preamp and preferred the Marantz with its room correction.  
Have my eye on Benchmark DAC3 HGC or LA4 or possibly the Bel Canto DAC 2.7. So the potential is to insert a preamp and change the DAC, or just a preamp.

I am generally very happy with the sound but it might be a tad sterile. Would welcome a tincture of warmth without losing clarity and dynamics. Do not want to fuss with tubes.
But the Cambridge DAC seems pretty darn good. Will I hear a difference. My plan is to auction two of these in home, but which two? Opinions please. 
I'd go for the auction. Bidding wars can drive price higher than you'd think.
A new DAC may help, but IMHO, your Marantz may be the problem with your 2CH enjoyment. The 8802 is about as good of a pre as any receiver can be, but still not a match for a good dedicated pre. I know you said you do not want to mess with tubes, I get that, been there, but I caved. I run a 6SN7 tube pre with a SS amp and the sound from the dedicated pre is in a completely different league compared to my Marantz receiver. Liquidity, soundstage, and that bit of warmth all on a new level. I lost some of the one box convenience, but it is about the sound so I do not miss it at all. The receiver has been working at TV duty only for a good long while now. Also lots of good SS Pre's out there too.
I think you may be right. Not that the Marantz is bad, but that it is more unlike a straight preamp. The Cambridge, bel canto, and benchmark DACs might each sound slightly different, but they are all good DACs.