Measuring RF transmitted Power

As-is, your first problem is that your circuit will draw crazy base currents from the BC369 PNP guy, as well as the 2N6488s. The 2N6488s certainly need a lot of base current here (100s of milliamps), but it shouldn't be as "unlimited" as your current circuit allows it to be. That's probably breaking the simulator's models, as it implies a tremendous amount of saturation charge which has to be cleared before the transistor can switch back off.

Here's your circuit in CircuitLab:

I've added a few resistors (R3, R4) to help control the currents a bit. Click through to the circuit page, run the DC and time-domain simulation, and you'll see closer to tens-of-microseconds switching times -- not the 500us you're seeing. Hope that helps!

EDIT: R4 isn't super important because there's already "feedback" from the rising base voltage. But R3 really is, because it sits between Q1 and Q2, both of which have their emitters tied to opposing rails, so they don't have that same feedback mechanism.

The breadboard may be causing issues, check your layout (especially the feedback section)

Also, it's possible the inductor you are using is not suitable - it says it's only rated up to 100kHz, so it's SRF (self resonant frequency) is probably pretty low. It may be causing instability.
Try changing it to one with a higher SRF (e.g. >500kHz), but still with suitable current capability.

I did mention the output cap below but abdullah is right about the input cap being important. It does depend on the load, but the whole loop from in to out should be as small and low impedance as possible, ideally using a ground plane. On a breadboard that's "difficult" ;-)
If the frequency problem is not there with a steady load, I think as Kit says it's an output filtering issue, since the switcher won't be fast enough to adapt to high di/dt changes on the output and there's no "reserve". Increase the output filter capacitance and see if the ripple drops, if it does that's almost certainly the issue.

EDIT - Ah, I see you tried it with a resistor on the output.
In that case it would seem it's not the filtering. At this point I think I would use a different method of prototyping that's more suited to a switching regulator. Also use another chip just in case.
Either etch a board or use dead bug style, or stripboard with very careful attention to layout. If the frequency is still too high I would assume it's part of it's operation and not covered correctly in the datasheet - if this is the case then an e-mail to OnSemi is in order to see what they have to say.

EDIT 2 - Okay, after more reading I think the sense resistor (possibly combined with the inductor issue mentioned above) may be causing the current sense to trip too often and increase the timing capacitor charging slope. This will likely appear like the oscillator is switching faster.
A relevant quote from the App note:

When this voltage becomes greater than 330 mV, the current limit circuitry provides an additional current path to charge the timing capacitor CT. This causes it to rapidly reach the upper oscillator threshold, thereby shortening the time of output switch conduction and thus reducing the amount of energy stored in the inductor. This can be observed as an increase in the slope of the charging portion of the CT voltage waveform as shown in Figure 5.

Your oscillscope waveforms seem to agree with this description. Also, if you haven't tried changing the inductor, do this and see how it goes, plus you could try not using the current sense (i.e. just connect to input voltage)