How do I appropriately/safely connect multiple power tools to a 20-amp outlet?
The answer to your last question is "Yes", it is perfectly fine to use a 15 amp plug strip on a 20 amp circuit like you have. That is why the slots on the receptacle go both horizontal and vertical. I'd suggest a plug strip with it's own 15 amp resetable breaker built in. That will protect your lower amp tools.

The second issue would be to build your own multiple outlet strip with a two gang handy box and two 20 amp duplex receptacles and a length of 12 AWG or 10 AWG SO or SVT cable terminated with a 20 amp plug.