If you can't access them from the same PS console while under a different PS account, that suggests that the saved appearance data is tied to the PS account. Because of that, you won't be able to access it from your new PS account.

My suggestion would be to use your old PS account on that same console and go to the login screen, then try to load that appearance data. You probably won't be able to do anything like transfer it to your new account, but if you can simply look at the settings you chose then you can write down your choices on a piece of paper, then re-make those saved appearances on your new account afterwards.

Even that might not work if the saved appearance data is tied to both your PS account and your FF14 account, but it's worth a shot!