Any sense of how hard it can be to track down the correct transistors for this model?
I have no idea what the circuitry of that amplifier is like. So I have no idea about that. Well, the fact that you are looking for transistors instead of ICs gives one a greater sense of optimism.
Do they need to be OEM or do they just need to meet the right specs?
They don't need to be OEM and will be fine if they are the right specs. If your tech person is good, then they can sometimes alter the circuitry to get it working well even if the transistors they get are a little different. If your tech is really good, you might want to ask about the cause of the failure, and if anything can be done to prevent such a failure in the future. And if they do have a way of preventing future failures, you might want them to modify the working one to prevent that one from failing. However, that is dependent on them being really good, and I have no idea how good your tech person is. And it may be that there isn't anything that they can reasonably do to prevent future failures. I don't know the cause of the failure or anything about the particular circuitry involved (other than it is an amplifier for low frequencies).
In case my previous comments about powered subwoofers seem cryptic, the reason I don't like amplifiers built into speakers is that I have had experience with the amplifiers failing in some of them, and I am not alone in that, judging from comments online in various audio forums (though I freely admit that some have been extremely reliable). I have never had one of the actual speakers fail in such a unit. With some built-in amplifiers, getting a schematic can be difficult and sometimes the parts are impossible to find. And since built-in amplifiers often have a response curve in them designed for the particular application (to compensate for frequency response problems of the speaker), putting in a replacement amplifier with a flat response is not going to get the thing working properly; the frequency response will be off. Usually, they don't advertise whether the built-in amplifier has a flat response or not, as they are selling you the package and the overall frequency response is what one hears about.
Also, separate amplifiers made by reputable companies are almost always very reliable. But the irony is, it is easy to just replace a separate amplifier if it does fail. Being separate is a good thing. Of course, being separate does take up more space and does add a little complexity for hooking things up.
To be fair (to continue with this digression), there is an advantage to a built-in amplifier, and that is that they can design it such that it will never overdrive the speaker, no matter what one does with the controls. They don't all do that, but if they do, it is a good feature to keep the owner from damaging the speaker with excessive power. With unpowered speakers and a separate amplifier, the person operating it can be an idiot and just keep turning up the volume control no matter how much it is distorting. And there are some idiots who do exactly that, and then wonder why they have equipment failure.
Anyway, I am glad you found a replacement subwoofer and that your tech is optimistic about getting replacement parts for the amplifier. You can then go back to enjoying your speakers once they are repaired.