The concept of Hell discourages belief

[catfish]

So, if aeonian was meant as "eternal", why wasn't the same word used everywhere?

Sorry to be frank, but that's a stupid question. Languages frequently have more than one word for the same concept. With regard to eternal life, we could say everlasting life and people would understand it the same way.

There are also indications of eternal punishment independent of aionios, such as their worm does not die and the fire is not quenched.

No problem frank, I didn't expect you to understand why it's a valid question regarding a Greek word that means "pertaining to an age" as being relevant to the discussion about the so-called "eternal" punishment of an ever-loving and ever-forgiving God...