If you want to going digital all the way through, then the JBL SDP-58 has Dante output capabilities, supposedly. You could then feed that in to a DSP of your choice (Qsys, Tesira, Dante+DSP amps...), over Dante and out to whatever your system uses (Dante amps, analog amps, active speakers, etc.)
I know that Biamp's Tesira Server IO's input cards have 4 channels of input each, and the output cards have 4 channels of output each. Each Server IO chassis can support 13 cards in any configuration. For your use case, you could configure it with a Dante or AVB card (if you want it), 8 4-channel output cards (32 total outputs), and 4 input cards for 16 inputs. You could theoretically remove the network audio card and add another input card for 20 inputs, but I don't recommend that because then you can't expand digitally in the future. One other configuration option is to use two Server IO chassis. In that case, you would use 2 Server IO chassis with AVB cards, and configure them with inputs and outputs to your heart's content. -- The Tesira programming software will auto-setup the AVB routes and distribute the processing as needed between devices -- The only issue then would be latency, as the native latency is around 1.5-2ms, and an AVB hop would add an extra 1ms. (I know that other DSP platforms can be faster, but I know Tesira so I'm sticking to it.)
The Server IO will definitely have enough processing power for what you need, but new it will definitely be over your budget, and according to random people on the internet, the analog audio quality on Tesira isn't as good as other DSPs. -- Though in my experience Tesira sounds and measures fine, and prices on the used market are really cheap.
The only other issue is with control. You can create presets and other things, but controlling Tesira without a windows computer or fancy Pro-AV control system is not trivial. However, if you take the time to build a GUI through Biamp Canvas, you can set up a PC to auto-connect when you launch the Canvas program, which can make controlling it much easier, depending on your needs. (In my case, I have quick access to mute buttons, level controls, and phantom power switches for my mic. If I want to make an EQ change, I have to go through the Tesira programming software.)
Just as a note, the Tesira programming software is freely-available:
They have a lot of resources to learn how to use it as well, also freely available. One thing of note is that the compiler will auto-add equipment and try to optimize for the lowest cost it can, if you just give it the program file to start with.
With the above in mind, I created a basic file with 32 inputs, 24 outputs, EQ and delay on all of them, and a matrix mixer between them all. The Tesira software claims that (depending on how you set up the system) you would be looking at 2-4ms of latency, and could theoretically fit what I created on one DSP-2 card inside the Server IO, with one external IO expander. You could also add more processing, you would just need to add more DSP-2 cards to the Server-IO, or use a Forte instead of the IO expander. -- The only thing to consider is that Tesira cannot make processing blocks across multiple devices. So in my system, since I have all I/O running through a single matrix mixer block, if I had more outputs, then the system would have to use an input device -> AVB -> DSP -> AVB -> output device. This would add more latency to all channels since the software automatically handles delay equalization, and you could end up needing an AVB switch if you have more than 2 AVB devices in the system.
So in conclusion, you might want to look at the Tesira line. I know some people use it for their home theater setups, and in my opinion, with balanced line level signals in and out they are audibly transparent, when configured properly. Biamp has a ton of resources available, so you should be able to learn what you need and make an educated decision.
If you have any other things, let me know.
