I had no trouble with Aloth choosing mostly benevolent and honest dispositions. By the time I had my ship at Port Maje I already had approval 1.
First of all you can activate in the settings that you see the disposition icons for the dialog choices - so you see if a dialog choice is intended to be honest, diplomatic and so on.
I think if you do not blow Aloths cover when you recruit him you already get some approval points from him. You can get a lot more points just by talking with him when you get the ship - for example when you choose the "how do we met again" choice you will get several dialog options to respond to the back story that he tells you.
You can get lots of points if you do his personal quest. If you want him to stay with you in the end you need to tell him at this point that he does not have to destroy the leaden key. At least if he is anti-leaden key - not sure how it is if he is pro leaden key.
But I noticed that he can loose points very fast - for example bringing Xoti to the temple so that she can release the souls seem to loose points with him. And asking Xoti why she doesn't stop collecting souls - for Aloth this is like telling her to stop being dutiful and he hates it. I think I went from 128 to 96 with him just for the few dialog options with Xoti.
Anyway, there is a mod that you can use to see the actual points and to change them if you like - meaning you can observe how a dialog choice affects your points and to change them and to give for example Aloth enough points to trigger the romance.
I think for the romance you need approval 2 and you have to visit the ashen maw island.
Here is the link for the mod: https://www.nexusmods.com/pillarsofeternity2/mods/2