OK. I'm still enjoying my first cup of coffee, so bear with me.
Let's discuss a specific example so we do not get lost in the miasma of complicating variables. Since you linked to a Cooper Discoverer M+S winter tire, let's stick with that tire.
The Cooper Discoverer M+S winter tire in the size you are discussing is a Standard Load ISO-Metric tire 255/70R18 with a Load Index of 113. Following the procedure outlined in the Toyo Guide, this tells us that in order to use this tire on an LC200 which requires a tire with a Load Limit of 2513 lbs, we need to inflate this tire to 36psi which gives us a Load Limit of 2535 lbs which is the Maximum for this tire. So yes, if someone wants to use this tire on an LC200 they can if they inflate it to the maximum load pressure indicated on the sidewall of the tire. Is that best practice? I don't think so, but it is possible.
For this same tire, following page 466 of the manual as you cited, then when we divide the "maximum cold tire inflation pressure mentioned on the sidewall of the tire" (this is where I saw the reference, so when you say, "And I never referenced the max rating on the sidewall of the tire." I guess you are correct, you didn't reference it, but your citation from the manual did) which is 2535 lbs by 1.10 we get 2305 lbs which is, indeed, more than half the greater of the two GAWR of 4300 lbs which would be 2150 lbs. So yes, according to page 466 of the manual, the Cooper Discoverer 255/70R18 113 SL tire would be acceptable for use on the LC200.
However, if you are keen on following the manual, you should also look at page 467 where it states (emphasis mine):
●Snow tires
For driving on snow-covered roads or icy roads, we recommend using snow tires. If you need snow tires,
select tires of the same size, construction and load capacity as the originally installed tires. Since your vehicle has radial tires as original equipment, make sure your snow tires also have radial construction. Do not install studded tires without first checking local regulations for possible restrictions. Snow tires should be installed on all wheels.
This directive from the manual would suggest that a winter tire like the Cooper Discoverer we're talking about should be 285/60R18 with a Load Index of 116. Clearly, the Cooper Discoverer 255/70R18 113 SL tire does not meet these criteria, most notably the Load Index, so - according to the manual - would be unsuitable for use on the LC200.
You also mentioned P-Metric P255/70R18 tires, so let's discuss those tires.
In the Toyo guide (page 19), a typical P255/70R18 tire would have a Load Index of 112 and a Maximum Load of 2469 lbs @ 35psi. So, following the directive on page 466 of the manual, we divide 2469 by 1.10 which is 2245lbs and is more than half the GAWR of 4300 lbs. So, in theory, a typical P255/70R18 112 tire would be OK for use on a LC200 if inflated to the Maximum Load pressure of 35psi.
However, following the Toyo guide, it is not possible to reach the minimum required Load Limit of 2513 lbs for this typical tire, so it would NOT be suitable for use on the LC200.
Theory is fine, but let's discuss a specific P-Metric P255/70R18 tire like the Michelin LTX M/S2 P255/70R18 112T (see here on the Michelin site:
LTX M/S2).
This Michelin P255/70R18 112T tire has, according to Michelin, a Maximum Load of 2245 lbs @ 51psi. Again, following the procedure on page 466 of the manual, when we divide 2245 by 1.10 we get 2041 lbs which is less than half the GAWR of 4300 lbs and would NOT be suitable for use on the LC200. Also, following the Toyo guide, even when inflated to 50psi this tire would not reach the required Load Limit of 2513 lbs and would NOT be suitable for use on a LC200.
In conclusion:
At best, when examining the specifications of any specific tire offering, it may be possible to use some 255/70R18 tires on the LC200 if inflated to their Maximum Load pressure, but IMHO is not advisable.
It is important to understand the difference between an ISO-Metric 255/70R18 tire and a P-Metric P255/70R18 tire.
Although not discussed here, if one could find an LT-Metric LT255/70R18 tire it would probably be OK for use on a LC200.
When recommending tires for use on the LC200 it is best to discuss a specific tire offering than to generalize.
Finally, it is my opinion that when we take the contents of the Land Cruiser Owner's Manual in its entirety, it is reasonable to take the meaning as a recommendation to assure that any replacement tire have the same (or better) load capacity (read Load Index) as the tires which came stock on the vehicle.
Coffee's gone, so your turn