There are no configurations that "don't fail" -- except the configuration where there is no load present (and, thus, no need for power!).
My approach will be the opposite: remove things until it starts working.
Recall, everything worked last year. The extension cords and lights have been stored "indoors" for all that time. OTOH, the outlets have been exposed to the elements for the ~9 months (including a Summer and a Monsoon) since then. So, any "changes" are most likely manifest in those items!
Wiring inside the block wall is likely not at risk as it is safely hidden away (unless something likes chewing on vinyl!)
First, verify SWMBO's assertion that the toaster oven resulted in a similar behavior. If that's true, it *tends* to rule out the lights and the extension cord as possible problem areas (no guarantee, there, as they could have other problems, as well). Then, reattach the lights as the "nominal load" -- cuz I have lots of experience with them failing (I don't want to end up with a situation where things SOMETIMES work and that confuses any deductions made later).
[The idea of leaving an item used for food prep outside just doesn't appeal to me! :> ]Explore the upper limits on what the breaker will HOLD. If it trips (when it would otherwise have held, based on prior observations), I have another data point regarding the circuit's performance. Is any loss of capacity a likely effect of aging? Or, is it dramatic enough to suggest a fault, somewhere (keeping in mind that I'm using the replacement GFCI, presently). Can a regular (20A) branch circuit carry the same load without incident? (those breakers are OLDER, yet!)
Then, open all the Jboxes and have a peek inside. Any signs of "wildlife"? Moisture?
Beginning at the box closest (electrically) to the panel, look at hot-neutral, hot-ground, neutral-ground voltages under that fixed load (with breaker in the "holding" state). Any IR drops should scale linearly; regardless of how much wire there is between Jbox #X and Jbox #Y, there should be an identical amount of neutral, hot and earth conductors! I can do this from the exposed side of each receptacle -- no real effort required.
Then, start removing receptacles (in the hope that something may have set up shop INSIDE one). At the same time, examine the contacts on each: anything loose? Any signs of oxidation/corrosion?
Any changes in voltage readings when probing conductors instead of outlet contacts?
Ultimately, I'll have to remove the outlet into which the extension is plugged.
If this turns up nothing, start moving the load upstream. And, after verifying operation at each such point, isolate the downstream portion of the branch circuit (open wire nuts).
Eventually, I'll have a wire in the wall that connects the GFCI to the *first* -- and ONLY -- receptacle.