I use a password manager with 16 character random passwords for all my accounts. Currently, it's starting to get annoying to open my password manager, enter my master password, then copy my password manually to the The Old Republic client. Is there a way for the client to remember my password? Something like a hidden startup flag.
I use the KeePassx2 for passwords management and, from my perspective, it's not a problem to open vault and copy-past password, as it happens once a session. The flow is pretty much the same to what you described: master password -> copy -> paste -> press button.
As an option, you can roll with something like XKCD passwords scheme ("correct horse battery staple scheme") for SWTOR password and eliminate passwords manager as a step.
Also, I have two-factor auth enabled with Android app, so I have to also unlock my phone to get the security key. That's an extra step that also takes time.
Even if your new password is a bit weaker as a result, because as humans we're much worse at generating close-to-random passwords, two-factor auth will help you to keep your account secure enough.