A common thing is that the amount of gain/distortion/overdrive that sounds good to your ear is too much when recording.
Moving the mic toward the edge of the cone can help take the edginess down.
A low pass filter might help.
Okay, it wasn't clear that the AI outputs were tried without the transformers. I can't say I've had that problem.
I have had cases where a line output was too hot for a mixer's mic input, so it seemed like something to consider. Some of these newer digital mixers don't have pads on their mic...
I don't know if related, but piezoelectric pickups need very high impedance termination, on the order of megaohms. The high Z input on an interface might be enough, but I would check the specs. I generally use high quality active DIs for piezoelectric pickups.
"True Peak" is a kind of measurement, not a kind of limiting. A limiter might specify a target in terms of TP, but it can achieve that by whatever means. Heck, you can just decrease the gain and not change the dynamics at all.
I'm not sure if there are any modern limiter plug-ins that don't...
I have access to all kinds of plug-ins, but I just use the same two (an eq and a compressor) on channels 95% of the time, with two or three others for special cases.
If you can't capture that hiss, you could certainly replicate it, even without a computer. You might even be able to opt out of having the hiss when it suited you.
Sure. The Alesis HD24 is a good example of that. It doesn't have trim controls, but otherwise it's what you're looking for. Coincidentally, I have one for sale.
Most likely you need a USB audio interface to connect the mixer. Depending on the interface and how you like to record, it might completely replace the mixer. The USB mic may not get along with the interface, but you could try it. You will probably be better off with a proper mic that uses an...
There is no general "better" response. There is more accurate response and there is better response for a given source. They aren't necessarily the same thing.
The SM58 is fine, but the e835 is pretty nice, too. Different but nice, and affordable. I had issues with e935s, but I don't know that...
I described three ways to open Task Manager. Just open it, go to the Performance tab, run your MIDI thing until the problem appears, look at the graphs to see what resource maxed out. If the Performance tab isn't already showing a column of graphs down the left side, right-click to change it.
I'm not sure how helpful another pass through cassette would be. If you've got your mixes in the DAW, maybe work on making them cohesive using the excellent tools available there.
There are several ways to open Task Manager. Type it in the search bar, right click the Task Bar, type Win-X (using the Windows key) are three that I can think of.