Yup, that’s why I’m here. I thought that was the point of “IWTL”?

It is. In that case I'll recommend you go with a different project. Same as if it was IWTL how to make a small amount of Florine gas - sure, there's neat things you could do with that, but maybe stick to things not likely to cause a civil disturbance. You say it wouldn't effect neighbors but I'm kind of skeptical. A typical suburban noise floor at 1 MHz might be around -100 dBm. Apply the inverse-square law to divine how far your signal - if actually transmitted - can go.

Radio is really cool, I'm not trying to discourage you here, or be patronising. I'll say that I'd guess many commercial BJTs will work to amplify 1MHz in this power range, albeit with distortion. How to design a circuit that will be linear is something I haven't personally looked into much. I'd guess that the know-how to do that would amount to a good crash course in many of the other analog concepts you might need, like what near-field means.

Actually, that specific one might not be involved, so I'll throw it out there. An antenna needs to be 1/4 wavelength long, or it's not really interacting with waves, but just local fields. Something also within a fraction of the wavelength may feel the field (it's in the near field), but not much in the way of a wave will be produced off into the distance, for the same reason you can't flip or snap a rope with just your fingers. MW is defined as being over 100m wavelength, so any antenna below 25m is electrically short in those frequencies.

I have a NanoVNA so could build a small dipole. High efficiency isn’t really the point.

Efficiency might not be the point, but not frying your amp is good. Maybe your low-power amplifier can handle Watts of standing wave, but I wouldn't assume it. Like I covered, no small antenna will make a difference here.