Is it possible to modify the entry method on a goal that already exists?
(Generally) Yes, by contacting firstname.lastname@example.org
It depends partly on what you want to change it from and to. Some data entry methods are not compatible (in which case you’d need to start a new goal instead), and some don’t require the help of the support team (e.g. adding IFTTT can be done at any time; adding or removing Apple Health is all on your side; Beeminder->Beeminder links can be set up by you, etc). It’s probably easiest to contact email@example.com so we can take a look at the situation and talk it over with you, but I can’t promise it will definitely be possible!