Confused About Postage Due

first time IDing these postage due stamps...thought I had a J29 but not sure if it's really a later issue, J59?

I'm having a hard time distinguishing the difference.

This is from an 1924 album and I've noticed that many have been misidentified and mounted in the wrong spots. For a novice this very disconcerting. Are the watermarks the only way of differentiating between the two? And if so, how should I proceed?

Good question ..

Incorrectly mounted stamps are a common occurence
in older albums, especially childrens collections,
quite often even the country of origin is mistaken.
That's cool, gives you opportunity to check and learn
your stamps and mount them correctly.

A J29 is perf 12, a J59 is perf 10.
If it is a perf 12, there a whole bunch other ones it could be, but watermarking is the only way to figure it out. J38,J45 are those defined by watermarks.
On the J59, similar items (J52) is watermarked.
There is a perf 11 item as well, J61.

I would suggest that it is more likely a less expensive version than you are thinking it is. Always start low, then when it is worth more you can be happy.

You also have color varieties as in this link, which I have yet to figure out completely:

https://goscf.com/t/18075

US Postage Due varieties can be a tough speciality.