Word meaning "open to being persuaded by a strong argument"?

This meaning may not be the first that springs to mind when we encounter the word reasonable in isolation, but this is certainly among its available meanings, and in the right context the word will be read or heard as meaning thus. OED:

willing to listen to or prepared to see reason.

It seems you have explored all possibilities. I can suggest the following:

• "approachable"? - "The supervisor is quite approachable, so don't hesitate to bring up any problems you have."

• "accessible"? - "Talk to our director and you'll find he's accessible to new ideas."

• "open and responsive"?, "unbiased"?

I still think "receptive" fits better than any of my suggestions.

Convincible :

• being susceptible to persuasion.

Persuasible:

• Capable of being persuaded; persuadable.

• In a figurative sense you can talk about a permeable mind.

As for your sample sentence. ..... an unprejudiced attitude towards disagreement, might work!!

I feel like the word you're thinking of is 'pragmatic', as in 'pragmatic about his views'. A pragmatic person would be willing to change their minds if someone offered an irrefutable argument, rather than clinging to an untenable position.