Checking on the support page for the GoDaddy payments plugin (https://wordpress.org/support/topic/gdp-overrides-customized-place-order-button-text/), they recommend doing the strategy you are using but they noted that it only works when you also are using the "Say What" plugin (https://wordpress.org/plugins/say-what/) with certain settings that are no longer apparent.

You will very likely need to install the "Say What" plugin, find the text domain that GoDaddy is using, then replace the GoDaddy wording with your wording through the Say What plugin interface.

Potentially you could also hack up the GoDaddy plugin but I wouldn't recommend that at all as then you wouldn't be able to easily update it when security issues inevitably get patched.