What size mini split does a 300 sq ft bedroom in Idaho Falls, ID need?

Notes

• The "20 BTU per square foot" rule is a Midwest number. Idaho Falls runs 498 cooling degree days, which works out to 16.5 BTU/ft² — so for this bedroom the rule overshoots by 17%. A single national figure has to be wrong somewhere, and this is where.
• Bedroom: the room where oversizing hurts most — quiet, low load, long runtimes wanted.
• 6,000 BTU/hr is 21% above the load, and the gap between head sizes is wide — this is already the smallest head. In a single room that matters more than it would on a central system: there are no other rooms to absorb the excess capacity. If the room is well insulated and shaded, the smaller head is usually the better buy, and modern inverter compressors modulate down far better than they modulate up.
• Idaho Falls is dry — nights fall 36°F below the afternoon high, which only happens when there is little water in the air. Latent load is small, so nearly all of the head's capacity goes into temperature. A slightly undersized head is forgiving here: it simply runs longer.
• Do not forget the winter side. Idaho Falls designs to -5°F. That is cold enough that a standard head will have lost a large part of its rated capacity by the time it is needed most — check the manufacturer's capacity table at -5°F, not the nameplate, and look at hyper-heat rated equipment.
• Where these numbers come from. Pocatello Regional Airport, 76 km from downtown Idaho Falls, daily records 2015–2024. Design temperatures are calibrated against published ASHRAE values at eight airports and land within about 2°F of them.