LTspice Hartley oscillator wave packet / soliton is rectified on breadboard circuit

Are you using the "x10" setting on the scope probes? That's essential for accurate high-frequency operation without excess loading of the circuit you are trying to examine.
x1 connects the probe cable and scope input capacitance directly to the circuit and can often drastically change the waveforms or upset things in high frequency or high impedance circuits.

Alternately - or as well - add a 10:1 resistive divider (eg. 47K / 4.7K) after the output cap in both the sim and breadboard versions & see how that affects the final waveforms; it minimises the effect of load capacitance on the tuned circuit.

Do you have good RF decoupling across the power supply?

I revisited this problem by implementing the circuit with fresh components, including a ceramic 1nF capacitor, and the results are pretty close to what I get with LTspice: the waveform is a series of wave packets. Thus it appears that the discrepancy may have been due to a bad 1nF capacitor.

for what you are trying to do, a ceramic cap there is probably not such a great idea, a mylar is probably better.

I cannot explain the discrepancies that this thread was started to explain (bad components? faulty breadboard?), but with fresh components LTspice captures what I expect to see very well, and the results are not sensitive to capacitor type.

was it built on a breadboard? it's possible something wasn't making a good connection. i've had that happen a lot from oxidation on the component leads or the breadboard doesn't grab the lead very well.

when i was young, i lived in a humid climate (Boston area) and the springs used on things like the old radio shack 200 in one kits would gradually turn gray with oxidation. i would have the same problems with breadboards, but the contacts on the breadboards aren't visible.

i have built a lot of stuff using LTSpice, and 90% of the time it's almost exactly the same when built with physical components. a few percent of the time, it doesn't work exactly the same, and i need to mess around with component values. about 1-2% of the time it either doesn't work at all, or is so far off it's no where near working right.