Its the transformers. HF tuning and stability depends hugely on the specific iron in use, so whats used on 8800 transformers may not quite apply here.
Well, yes, and no- let's clarify a little here.
@HepGreg - you have absolutely nothing to fear from using the stock transformers with Dave's design, or using different/better transformers. Better transformers = better stability. Plus, I'm also hoping to get you to use that new scope a little more. Besides- the stock 4 ohm transformers in these VOM amps are supposed to be pretty good- I'd give them a go before ripping them out of there. You might just be impressed.
What we are talking about when it comes to HF tuning and stability:
First is the amount of global negative feedback to set the amplifier sensitivity- this is set by the feedback resistor. Assuming we're talking about Dave's front end as in my schematic I posted (with RF input filter, and 100 ohms between the joined cathodes both sharing the feedback resistor for biasing), Dave used 1.2K for the 8800's crappy stock 4 ohm transformers (first schematic below) and it was stable. This will be no different for your 4 ohm stock transformers. Dave used 1K with a really nice 8 ohm Z565 type output transformer (second schematic below) and it was even more stable. This value will be the same for just about any 8 ohm transformer unless it's even more cheap/crappy than the stock iron. So no worries there, these are all very safe, proven values that will not cause instability.
When we are talking about High frequency tuning, this is not about oscillation, that's next. HF tuning IS transformer dependent, (the resonant frequency and damping characteristic of the transformer is a big factor here) and is about optimizing the 10kHz square wave performance for the best appearance, referred to as "transient response". With just a feedback resistor and no "phase advance" or "frequency compensation" cap parallel that feedback resistor, when using a crappy cheap or bad stock transformer, your 10kHz square wave will look more or less like that on the left. Ringing, ugly, but NOT usually unstable. With the proper selection of compensation cap, you can tame the transient response to look more like that on the right. Very easy to do with a scope. Usually a compensation cap is enough- if not, there are shelf/zobel networks or outright shunt capacitors that can easily be employed if we see a problem.
When you are talking about high frequency "stability", (the lack thereof becoming oscillation) this has much more to do with the gain of the circuit, the amount of cross-talk between your wiring, and most importantly whether high frequency limiters have been installed. I simulate what oscillation looks like in the .gif below where I am applying a capacitive only load on the speaker output and watching it go bonkers as I increase that capacitance. Good wire dress, and the use of that high frequency filter on the input (33K + 47pF filters out anything above 100kHz) is what ensures stability, not which transformers you use. (The only exception to this is if you are using so much negative feedback that the system becomes unstable, which is not at all a risk with Dave's recipe). Again, if this is an issue, we can address it with additional very simple measures.
So- I urge Dave's design with the 1.2K feedback, (A TBD compensation cap) and stock transformers to start- if you are still disappointed, then you can go with better transformers with very little tweaking.