The kitchen circuits themselves are perfectly legal: they have more than one 15A socket on each 20A leg. The requirement is because the circuits may have *multiple* high-draw appliances on them, not a single big fat 20A appliance, so it perfectly complies with both the letter and spirit.
As for the range plug, I use the oven enough that it would be too much of a PITA, plus the thing's buried behind the oven.
The only reason a UPS needs a bigger plug than the load is because it needs to charge the batteries while the load is running. If you can charge them from a *separate* circuit, you can split the combined load.
The extension cord option relies on the outlets being "sneaky 20As" (because they *are* 20A outlets with a 15A faceplate) and putting a "15A" plug on the wall end of a big fat 20A-capable extension cord and just plugging the UPS into that instead. Basically making a really long adapter, since everything in that chain *supports* 20A, they're just physically configured to not "allow" it.