Clarification on amplitude of observed NFC PICC response
Based on your description, it sounds like you have a third coil being used to monitor the traffic between the reader and the tag?  When you say a 'simple pickup coil', this makes me suspect you have what is essentially some wire you bent into a loop by hand connected to your oscilloscope?
NFC is a technology for the communication between exactly two devices and two coils.  Active load modulation works by altering the impedance of one of the coils, causing change in what gets reflected back to the primary coil - the coil in the reader.  You cannot use a third pickup coil to monitor the signal.  At best, you're monitoring what the signal is in that third pickup coil which depends on all kinds of factors, and at worst, you're doing that but also heavily altering the behavior and signal in the other two coils at the same time.
The only way to observe what the signal is in the reader's coil by connecting your oscilloscope to a tap directly on that reader's coil.  You cannot introduce a third pickup coil and expect to measure anything other than timing with NFC, or any near-field interaction for that matter.
Near-field relies on non-radiative coupling, so either electrostatic or inductive (as is the case with NFC) coupling.  This means that it is more accurate to think of an NFC reader and tag pair as a single air-cored transformer than a typical RF transmitter and receiver.
The near-field is heavily influenced by everything that is nearby.  When working with far-field radiation (radio waves), using a third antenna to monitor communication between two devices is perfectly acceptable.
However, you cannot do this with near-field coupling.  Where a third antenna is (unless positioned incorrectly) not going to have any impact on the radiated and received energy of two antennas of interest that you are monitoring.  When working in the near-field however, introducing a third coil is going to have a profound effect on the signal the other 2 coils see, and also cannot be used to easily infer or measure what the signal the other coils are seeing actually is.
So if you are using a third pickup coil that you've introduced into this system, the only thing you are measuring with your oscilloscope is what is being induced in that coil.  It is not representative of what either of the other 2 coils are themselves picking up, at least not at the level you are trying to measure.  Such a setup is really only useful for seeing if something is happening at specific times, but you certainly can't use such a setup if your intent is to look at things like amplitude in a coil other than the one connected to your oscilloscope.
Indeed, you say that the trace from the PCD to PICC looks exactly as expected, but I beg to differ.  It looks quite incorrect to me.  The expected trace does not have large voltage spikes that overshoot the carrier by 30-40% at the start of each transition like your trace has.
For whatever reason, you've chosen to ignore these spikes in your first trace, then have chosen to not ignore them in your second trace.  In both traces, the amplitude briefly exceeds the carrier at the start of each transition, and both traces are incorrect.
The reason for this is, of course, due to how strongly all participants in the near-field region interact.  Your third pickup coil isn't really just some sensing element, but rather you've essentially added an entire extra winding to an air-cored transformer, adding a lot of inductance that isn't supposed to be there, loading the other 2 antennas, stealing and storing some energy in its own self-inductance, moving resonant frequencies of everything to something else, and even if it did not have such a huge influence on the other two coils, what you measure in that third coil is not representative of what is seen in either of the other two coils.
In this specific instance, it appears that your third pickup coil is adding a lot of inductance to the system, and as soon as the induced current undergoes a sudden drop (the start of your transitions), the voltage in the third loop connected to your oscilloscope spikes then rings (as part of an LC tank with parasitic capacitances), and it takes a few cycles to extinguish.  There is no excess energy to dissipate when the transition is the opposite direction though, from less current to more current.  So you get spikes but only on the more to less transitions.  This is just a guess, near-field interactions get extremely complex so the true explanation is likely not so simple, but I hope it conveys at least how much room there is for the third coil to influence or at the least not accurately reflect what is going on in the other coils.
You must connect your oscilloscope to the reader's coil if you want to monitor the signal.  That is the only way.  And you need to be careful about how you connect the oscilloscope to that coil.  Ideally, you want to use an evaluation board that has the reader's coil broken out through a connector for the purpose of observing the signal with an oscilloscope.
You can ignore the signal generator of course, but this is what your test setup would need to be similar to:

Source: Rohde &amp; Schwarz PDF