In one of my previous logs I mentioned it to have been easier with a scope and that's what I got now.

Kind of. I bought myself an EspoTek Labrador, a small and extremely affordable USB Scope/Signal Generator/Power Supply/Logic Analyzer/Multimeter. Of course, for less than €30 you can't expect the world, but it is extremely portable (about 35x35mm) and pretty easy to use combined with the software that is downloadable from the EspoTek site (available for Linux, Windows, Mac, Android).

The scope also finally allowed me to get some nice plots of the Marantz remote output and get some better data on voltage levels and frequencies.

See below a plot captured by the scope. I sent a command (mute I think) with the remote to the amplifier, which showed up nicely. There is a small slope on the falling edge due to a small capacitance.

Connecting a 10kOhm resistor between the signal and ground completely removed the slope, but also lowered the signal voltage a bit. You can see that in the picture below. Same command has been sent, but the control bit (3rd bit) to differentiate between separate button presses is now flipped.

It was interesting to see that sometimes some peaks were missing on the plot. Apparently, the IR receiver didn't process the command correctly from the remote. As I wasn't position near it, it probably just didn't see part of the signal. In these cases, the receiver would not just show a shorter peak, but wouldn't signal anything at all, which is actually pretty reliable! As you'd hold down the button anyway, the command is repeated every 115ms, so that is typically not a problem from a user point of view. It is bound to be picked up at some point.

Conclusions from the measurements

As expected (as the Marantz control circuit is supplied by 4.9V), the output on the remote ports is just below the control circuit voltage at about 4.75V. For sending signals to the Marantz, using a 5V supply with a diode in between is perfect. (But as noted before, 3.3V also seemed to work with mine. But, n=1.)

The carrier frequency of the remote control (not necessarily the IR receiver!) is 36kHz.
The total time to send one command was 24.16ms. In this time, 13.5 bits were sent, as the start bit starts with half a bit of silence. And each bit takes of 64 cycles of a carrier burst, so:
Not exactly 36kHz, but close enough. I don´t know if the error comes from tolerance in (or age of) the remote, the scope or just selecting the wrong pixel when placing the cursors on the plot, but that doesn't really matter. As mentioned before, there's a lot of tolerance on the input and my Marantz still worked when I set my uC to 38kHz. But, for now I will leave it a 36kHz, as that also works and seems to be expected.