Floyd, you got the general idea that the higher the amplifier output, the greater the strain on the amp, mostly due to the fact additional amplifier output generates additional heat and reduces amplifier stability. At a certain point, the heat produced by the amplifier exceeds the heatsinks ability to remove and dissipate the heat from the amp and could go up in smoke. Furthermore, the heat/cool cycles are more extreme which reduces amplifier life.
You also understand that running multiple drivers in parallel lowers the ohms load. Your computations are close although 3x 8-ohm woofers in parallel = 2-2/3 ohms and 3x 4-ohm woofers in parallel = 1-1/3 Ω.
However, the Ω is a unit of measure of resistance. Therefore, higher numerical Ω = higher resistance. IF 1 Ω = 1-unit of measure of resistance. Accordingly, 2 Ω = 2x resistance. Therefore, higher Ω = higher resistance.
On speakers, we generally don't use resistance which is a DC measurement. Instead we use Impedance which is used with AC (music). Impedance IS resistance coupled with reactance. Impedance = (resistance + reactance). So if resistance increases in that formula, then impedance will also increase. This is the reason why speaker drivers when measured with a meter almost never coincides with it's impedance spec., almost always lower (an 8-ohm impedance driver could measure 6.8 ohms resistance). That's because we are measuring DC resistance of the coil which is not the speakers impedance.
Now, it would seem natural that a higher resistive load should increase strain on an amplifier since it would have to work harder on a higher resistive load right? But an amplifier doesn't work like you or I and get tired or fatigued. Instead, it's all a mathematical computation and increasing impedance simply ends up reducing the amplifier output, which means less current passes through it, so it does not heat up as much. Lowering the impedance means current has an easier time passing through the amp and this increase in power is what causes high heat and therefore strain on an amplifier. It's not strain like you or I lifting a sack of potatoes.
I think where some confusion comes is that 3 speakers combined, each possessing a certain amount resistance, might seem like the total resistance therefore increases. And this certainly is true in a series connection. But in a parallel resistance arrangement, I think the following analogy might be better: think if the speakers impedance is represented by hoses. If you blow through one, there is some resistance. But if you put 3 of them in your lips and blow through all three at once, you will observe far less resistance because the "air charge" has 3 alternate paths it can travel. On the other hand, if you connect the hoses end to end, the blow effort will increase. Therefore, in parallel, resistance is lower and if resistance in series is always higher -- either form of connection can be predictably calculated via a mathematical formula.