Dearest Streachy,
Your wee box is powering several north American freedom outputs and one that I know of is in North lands.
I didn't want to insult you because the wee box in my lab is doing well. The passband is FM grade. The Output is as specified 15 watts and the so called frequency drift I checked yesterday in my growing electronic lab. The crystal is essentially inside a wee phone booth closed and when initial power , it (the crystal) heats a bit and I tracked about 250 hertz down as the wee box comes up to oven temp. I am amazed some of the people here have accused the wee box of drift. No so, and every crystal is temp sensitive. I used to work in my youthful days at a BC band transmitter operator Gates Pre WW2 10 kw and it had an oven heater for crystal that NEVER was turned off. I think the approximate 200 or so hertz is indeed nominal and anyone who is listening in the mode of the wee box AM will not have to track anything. I mean 200 hertz drift. Not bad Old Boy.
The drift is indeed thermal, it's pretty easy to see this if you plot out the carrier frequency over time. I've done this a few times and posted the results, it has the characteristic curve that looks sort of like a decaying exponential. Lots of drift at first, then things settle down. After about 20 minutes give or take, it has (mostly) stabilized. I typically see a 200 to 300 Hz drift when listening to these rigs. Since we're dealing with AM and not SSB, that's not a major issue. Worst case tweak the tuning frequency if you're running a tight IF bandwidth due to a weak signal. If the filter is open, you won't even notice it.
In the past I've plotted carriers of commercial AM stations, this post has a plot the 1490 kHz graveyard channel:
https://www.hfunderground.com/board/index.php/topic,23649.0.htmlYou can see dozens of stations there. Many have interesting sawtooth style patterns, likely due to either thermal regulation or possibly even the PLL circuitry in the oscillator. Those patterns and frequency offsets can actually be used to ID MW stations by their carrier characteristics. Note the rather tight regulation, nothing is changing by more than a few Hz. Of course this level of frequency regulation isn't necessary for what operators are doing, just an example of what is possible. Some pirate stations do indeed have tight frequency regulation, as I've noticed when listening to them and watching the carrier frequency.
I have no firsthand experience with one of these 43m transmitters, but from the photos I've seen, the crystal is inside the box, and as digitalmod notes, it heats up as the transmitter runs. The IC chip used as an oscillator (I think LuLu transmitters tend to use a 74HC240?) also heats up, and stray capacitance is going to change, effecting the loading on the crystal, and the operating frequency. Plus lots of lower order effects we don't even think about. In a former life I worked in Industrial Process Control, specifically the use of beta/gamma/x-ray radiation to measure the thickness of metals, plastics, etc while being made. We used various radiation sensors, all of which had temperature sensitivity issues, so I've had some experience with these kinds of issues. We'd use an assortment of methods to keep things relatively thermally stable. Did I mention our sensor was sometimes a foot or two away from orange hot steel in a rolling mill?

Some other transmitters of this style (Radio Animal's Grenade is generally considered to be the first popular such rig) had a socket for the crystal, which was mounted on the outside. I think Channel Z's transmitters are this way as well. I'm sure this was initially done so operators could easily switch out the crystal to change frequency (plus these were the giant WWII surplus FT-243 crystals). But the added advantage is that the crystal is now outside of the transmitter box. So it does not tend to heat up as much, resulting in significantly less drift. The choice of crystal is going to have some effect, lower tempco crystals are available, but for a price.
A PLL inside one of these rigs is still going to drift, because it's got a crystal lurking somewhere in the circuit, as a reference frequency. Of course you could always use an external GPS derived 10 MHz reference if you want nearly absolute frequency stability, but that's overkill. I don't see anyone doing that. Well, OK, I see redhat and one or two other ops doing that

Another thing you can see when you peer closely at the carrier of some of these rigs is FMing. From the schematics I've seen, these LuLu style transmitters use a 74HC240 logic IC as the oscillator.The slightest change in the voltage applied to the IC affects the operating frequency. I use a 74HC02 in my little 22m circuit, so I've had first hand experience with that. As the transmitter is keyed with CW (even on other gates in the IC) there's a slight shift in the operating frequency. The only way to prevent this would be to have a separate IC dedicated to the oscillator, and take great care to regulate the voltage. And even after doing that, you also need to deal with ground bounce/shifting issues. A ground plane on the PCB is not always a solution here, you might need a separate ground plane/system for the oscillator IC, with local regulation. It's not a trivial issue.
If you watch the carrier while the station is on the air, you'll observe two things. When there's no modulation, the carrier is narrow, as you'd expect. When there's modulation, it becomes extremely wide and variable, due to the carrier frequency moving around with the audio modulation. Likely because the power supply voltage and/or ground is moving around with the modulation. Dedicated voltage regulation and careful treatment of the ground of the oscillator and its connection to the rest of the circuit is required to reduce or eliminate this. As a practical matter I generally don't notice significant audio distortion due to this. Generally the issues I observe as a listener are either over or under modulation, but that's a station setup issue, not a flaw with the transmitter. IIRC, the Grenade had a rather clever built in compressor/limiter that involved an LED and photoresistor, to act as a sort of AGC. As a result, it was much more tolerant of input audio level settings.
None of this is meant as a criticism of any particular transmitter, only observations from the point of a listener and frequency measurement nerd.