5.1 Decoder and Amplifier
This is a little different, I know, because I'm not trying to drive a set of headphones off a computer. :-) What I'm trying to do is get rid of the receiver in my 5.1 laser projector setup. What it seems I need is a 5.1 decoder to either pull from the digital output of a DVD player or decode on passthrough from HDMI, then a 5.1 amp to drive a set of Polk Audio speakers. I can't seem to find such a device -- all the DAC, decoders, etc., I can find assume stereo, and assume driving a set of headphones. The other end of the spectrum is full featured receivers with HDMI switching, all sorts of bluetooth capability, etc. I know I could buy a "sound bar," but, really... I have the space and wiring for a good set of 5.1 speakers, so going to a "sound bar" to replace well placed speakers seems like it's just... silly. Any ideas on how one can set this sort of thing up?

What you are looking for is a HT pre-amp/processor. The days of the simple 5.1 surround decoders are long since past. It will be cheaper to pickup a receiver with 5.1 in and out than most processors these days. About the cheapest full function HT processor that I am aware of is this: https://emotiva.com/collections/processors/products/mc-700 You can get some Denon/Onkyo/Yamaha with pre-outs for sub $600. If you need analog in that is an almost dead feature so somewhere around $900 is typically as low as you will find those.