Best Affordable 5.1 AND Stereo Receiver to Drive Meadowlark Heron-i Speakers

It sounds like you have that B&K Reference 30 (which is a HT preamp/processor) AND a separate amplifier.  Based on your tendancy towards "warmer" sounding equipment, I would look at the Bryston SP3 HT preamp/processor to replace your Reference 30.  There aren't any up for sale now, but I think I have seen them in the $3-4k range.  The Bryston SP3 has excellent power supply and fully discrete Class A analog audio stages.  However, for my own HT tastes, I found it too laid back in the midrange.

I would actually completely disagree with millercarbon's opinion that "HT is just a wasteland of bad audio" and "you will find there are no multi-channel anything that sound good".

With those speakers and the sound quality you're used to you will find there are no receivers anywhere close. In fact if you compare you will find there are no multi-channel anything that sound good. HT is just a wasteland of bad audio. No matter how much you spend! 

My system is dual use but very high end. The solution is to use the HDMI direct to your video. Forget surround, that's where all the bad sound is coming from in the first place, and feed just the L/R to your integrated. Exactly what I do. You won't have surround but you won't miss it because the money you save on amps, cables, and surround speakers buys you stereo sound that more than compensates. Especially when that is what you care about most anyway.

My advice, keep what you have and with $3k of your $4k budget add a Swarm/Distributed Bass Array type subwoofer system. This will be a huge benefit to both music and movies. Then with the remaining $1k upgrade your weakest wire and if anything is left after that then some Blue Quantum Fuses or HFT, depending on how much is left. Together these will transform your system in the direction of "you are there" palpable imaging and immersive, articulate, powerful and deep bass like you never heard before.