I have OPC 2.4.2 installed.

Just re-installed the old Square Module and made changes to checkout_payment/jscript_square.php - as documented in OPC 2.4.2 instructions.

Change
PHP Code:
if ($payment_modules->in_special_checkout() || empty($square) || !$square->enabled) {    return false;} 
to

PHP Code:
if ($payment_modules->in_special_checkout() || !defined(MODULE_PAYMENT_SQUARE_STATUS) || MODULE_PAYMENT_SQUARE_STATUS != 'True' || (!defined('MODULE_PAYMENT_SQUARE_APPLICATION_ID') || MODULE_PAYMENT_SQUARE_ACCESS_TOKEN == '')) {    return false;} 
Run through the set up of the old module, and as far as I can see, it successfully takes the payment and records the order in the admin.

Thanks to Cindy (lat9) for recommending this change.