GFI outlet vs breakers, maintenance needed
This is a vacation house in a resort community and we rent it out. We visit it at least once a month.

FYI that means you can't do your own electrical work and must hire an electrician, in nearly all jurisdictions. Many will allow &quot;trivial&quot; work to be done by landlord or tenant, such as swapping receptacles or switches for aesthetic/GFCI reasons, or changing light fixtures.  (although this forum is thick with cases where those tasks were not trivial at all, lol!)

I was unable to find a new replacement GFCI outlet of the correct color and amperage

For amperage, 15A receps are fine on 20A circuits as long as there are 2 or more sockets on the circuit.  NEC 210.21(B).
This is notched into Code for precisely this reason - to reduce the SKUs a store or electrician must carry. You only need a 20A recep if you have an appliance with sideways neutral, which means it's too big to use a 15A circuit.  We're talking BIG microwaves or really old window A/C's. For a tenant, tough beans.

for what passes for hardware stores there. And after driving 30 minutes to the closest Home Depot I discover they are out of stock as well. This kind of thing is not uncommon out there and it is typical that I have to buy parts in advance from the city I live in before visiting. So I replaced the outlet with a standard outlet.

Wow.  Well, avoid the daylights out of amazon.com. It's thick with counterfeits.
Downgrading the protection means you absorb all the liability if an injury occurs. Your insurer will probably even back out on those grounds.

Now I am trying to decide how best to repair this setup. The first obvious answer is to replace the outlet with a GFCI. But I really dislike that because my experience with GFCI outlets is that they are cheaply made mass-market devices that sometimes nuisance trip, and they introduce additional mechanical failure points.

Well, aside from the blatant counterfeits on Amazon, you generally have 2 tiers: &quot;builder grade&quot; and &quot;Spec grade&quot;.  Builder grade is for when it only has to work until you clear escrow :)  Spec grade are for when it's your building and you'll be responsible for total life-cycle costs.
You can guess which one we like around here.
A GFCI recep has exactly the same failure points as a GFCI breaker.  Point for the breaker, they tend to be made by Tier 1 manufacturers like Schneider, GE, Siemens.  Point against them, the breaker is a rather small package, especially a 3/4&quot; wide QO.
I have a &quot;QO&quot; GFCI breaker I am ripping out, because the darn thing won't tell me if it was a GFCI or overcurrent trip.  (the newest ones can, but their UI is very, very balky). For half again the price of anyone else's breaker they oughta be able to afford a 1 cent LED.

The advantage of leaving the breaker as is, is that if the GFCI in the wall triggers it won't kill the power to the refrigerator and range.

Yup, exactly. You should do everything in your power to keep refrigerators off of GFCI and AFCI.  I'm a huge fan of EMT metal conduit, which basically moots AFCI; and grounded fridges do not benefit from GFCI in any way.  That's a tough sell for a fridge in a garage or basement because all receps there are required to be GFCI, but your AHJ is able to grant a variance for a dedicated 1-socket/simplex &quot;Fridge only&quot; outlet.
If it's a dedicated circuit for the fridge, that's ideal; however if a circuit has only one socket, socket and breaker must match.