Yup, on MAMP Pro, I still get fatal error:

Fatal error: Uncaught exception 'Guzzle\Http\Exception\CurlException' with message '[curl] 35: Unsupported SSL protocol version [url] https://api-3t.paypal.com/nvp' in /PATH_TO/local/perch/addons/apps/perch_shop/lib/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php:359 Stack trace: #0 /PATH_TO/local/perch/addons/apps/perch_shop/lib/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php(292): Guzzle\Http\Curl\CurlMulti->isCurlException(Object(Guzzle\Http\Message\EntityEnclosingRequest), Object(Guzzle\Http\Curl\CurlHandle), Array) #1 /PATH_TO/local/perch/addons/apps/perch_shop/lib/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php(257): Guzzle\Http\Curl\CurlMulti->processResponse(Object(Guzzle\Http\Message\EntityEnclosingRequest), Object(Guzzle\Http\Curl\CurlHandle), Array) #2 /PATH_TO/local/perch/addons/apps/perch_shop/lib/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php(240 in /PATH_TO/local/perch/addons/apps/perch_shop/lib/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php on line 359

as per my first post in this thread.

So not the same error, but still an error, and I have a hunch that if it worked locally it would also work on my dev and live servers. Any clues? Pretty close to ripping out the Perch Shop stuff and just using PayPal Buy it Now buttons as a route to getting this working - not as neat, but may be the solution to getting this out on time/budget.

Having Googled the error that comes up locally, I came across this post https://forum.grabaperch.com/forum/05-10-2016-paypal-express-checkout and I tried the CURL test code

<?php
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, "https://tlstest.paypal.com/"); 
var_dump(curl_exec($ch));

This returns false locally, but is successful on the dev server, so perhaps there are two issues going on here.

The site is not yet launched, however the dev server is the same as the production server.

Yes, I am trying to focus on that issue but not getting anywhere... Do you have any other suggestions as to things I could try? Simplest possible test cases, or ways I can narrow down what the problem is?

Yes, I don't think you can get API details without having API access turned on. The PayPal account interface has been redesigned since then so it's hard to follow their instructions exactly.

I was pretty careful in setting this up and checked my shop.php config file a number of times and tried with numerous credentials, including those that let me checkout with the Expression Engine site I mentioned and got the same result each time.

In the end I've abandoned Perch Shop as I just couldn't get it working. A shame, and all was going fine until the checkout issue, but I couldn't get past it after trying on and off for over a week. I'm using the Perch PayPal Shop app instead, and it's looking like it will meet my needs for this very simple site.