Note that the links should take you to threads on TMC that include photos of the layout. Use your own judgement as to whether these locations are viable. Obviously no guarantees that they'll work, so if you have trouble please come back and edit the wiki for others.
Category 1: Unhitching not necessary
---United States---
California
Eureka
Category 2
Fountain Valley
One possible location which might block a couple of ICE/flex spots.
Hawthorne
Pull through spots but a very tight parking lot with lots of SpaceX and Tesla traffic. Not recommended but possible.
Mammoth Mountain
Back to back stalls may require parking on the outside and pulling the cable through.
Manteca
Pull through spots in a mall parking lot. Trailer would be an annoyance in the lot, but the spots are far from shopping so it's possible. Note also that the spacing on the obelisks seems tighter than in other pull-through locations.
Petaluma
Back-to-back pull-through chargers. If you park in the spots on the north side of the chargers, you could take one of the Supercharger cables and still not block the second space.
Rocklin
Pull through stalls, may allow outside cable or by blocking a single charger.
Tejon Ranch
Plenty of space behind any of the chargers for vehicles to maneuver.
Colorado
Trinidad
One end pull-through spot has plenty of clearance behind it for a trailer.
Idaho
Twin Falls
Appears to be a single pull through charger that would work.
Indiana
Indianapolis
End charger is pull-in and the charger is in a hotel lot.
Kentucky
London
End charger is pull-in and it's in a visitor center parking lot.
Maine
Augusta
1 pull-in spot. You'd be blocking an end of an aisle, but it's (currently) in a little-used area and it would easy to get round the other way. Other notes in post below.
Montana
Butte
The end charger has a vacant space next to it that appears to be workable.
New Mexico
Santa Rosa
Pull through chargers, two look doable, and in the linked photo someone has a trailer, so it's definitely possible.
Ohio
Cincinnati (Blue Ash)
End charger is pull-through. Trailer would have to be short and angled in order to avoid blocking the roadway.
Oregon
Bandon
4 pull-through, easy Category 1 based on your classifications
Sandy
There appears to be a single charger at this location that is usable by an MX hauling a trailer. The remainder are back-in.
Springfield
Category 2- 8 chargers, plenty of parking to unhitch, easy on/off I5
Woodburn
Category 2- 8 chargers, parking but often pretty full,adjacent to an outlet mall
Texas
Denton
At least the far left can be used (though it blocks some distant parking spots).
Washington
Ellensburg
One charger that would marginally, but not completely block the lane.
---Norway---
Nes i Ådal
Room for 4 cars with trailer without blocking access to remaining chargers.
Additional photo.