I think you have some decisions to make.
If you ever really go multichannel, it is worth being sure that each channel is level matched at the listening position. That is, they all are equally loud. You also want each of the speakers to have the same or similar frequency response and off-axis behavior, since they all work together to create the sound field. If you use the same amp or type of amp and same speaker on every channel, that helps make the job easier. Because of the physical layout of a person’s room, and because of budget constraints, the ideal is not always possible, but the closer to the ideal you can get, the easier the set up will be, and the better the result will be.
The people making the games, movies and other content have all worked together with the people who distribute content on discs and on line, along with the folks who make the home audio-visual gear, to ensure that they have at least some control over the prevention of piracy and other measures to help support profits. When people get together with a common goal and work hard and long at something, they often succeed, as is the case in the situation we are discussing. That is why the situation exists currently. It is possible to use a PC for many of the things we would like to be able to do, but not all. The same can be true of an AVR. There may be some things you can do on a PC that are harder, or not possible on an AVR. So you have to choose one, the other, or both. For the reasons you mention, an AVR is the easiest and cheapest route, with the fewest limitations, at least for most applications, and within most budgets.
You already have a two-channel DAC of excellent quality, an amp that will accept an XLR input, and a PC. You can try to use those with splitter cables to connect the DAC to your amp and sub at the same time. You need one splitter for each of the left and right channels. Then you’ll need adapters to match the XLR output of the splitter to the RCA input of the sub. You have a low-pass filter on your sub, so that’s good, but you’ll have no high-pass filter for your mains, and you may spend $50 to $100 or so for all the wires and adapters. Still probably the cheapest.
If you get a two-channel DAC with RCA and XLR outputs, you still won’t have a high-pass filter for the mains. You’d just eliminate the need for splitters and adapters.
So the next cheapest that has a real advantage, and is an actual step up, may be the used AVR, since that will give you the high pass for the mains. You already have a low-pass built into your sub, and many AVR’s can also do the low-pass part, so that’s also covered. Since you have a power amp, you may already have passive speakers. If so, you can use the amps built into the AVR directly to the passive speakers, or you can use the pre-outs of the AVR to the power amp input. In that case, if the AVR pre-outs have RCA connectors, and the power amp inputs are XLR only, you will need an adapter to match the two. As far as choosing whether to connect the passive speakers to the power amp or directly to the AVR, I would choose the one with the most watts.
As long as your AVR has pre outs as well as speaker connectors, it is your choice as to whether to go with active or passive speakers. Both will work. And yes, you can mix and match, with passive L and R and active surrounds, or whatever, and it will work. But it will also be fussier and more difficult to balance correctly if you mix and match.