Each collated research is worth 2.5 echos, and it takes ~58 actions to get 20 of them (or a return of ~.9 echos per action) useing foxfire candles and item conversions, I think that there are other ways to get them easier too besides fidgeting writer, but I am a but unsure of how cost effective they are.
Its pretty hard to calculate the exact return on the case of the figiting writer, due to the combo of having to use goods for every step, the fact that there are multiple steps that you can fail at, and the fact that the difficulty level is different for every step even if it uses the same description.
Assuming that you succeed at both steps, its obviously quite nice, giving you 5 echos worth of goods for 3 actions and a echo worth of goods (aka a return of 4 echos per 3 actions or 1.333 echos).
So it would give 20 collated research for 30 actions and 10 echos.
However if you have a failure rate of ~50% (which you do with the first step succeeding 75% of the time and the second step suceeding 70% of the time), the its pretty obviously not worth it.
I will assume that the first attempt you fail at step one, the second attempt you fail at step two, and the third and fourth attempt both succeed.
First and second time use up 1.5 echos worth of goods and 3 actions.
Third and forth use up 2 echos worth of goods, grant 10 echos worth of goods, and use 6 actions.
That is a total cost of: 3.5 echos, 9 actions and grants 10 echos worth of goods. Which is a return of .65 echos per action.
It really does depend on the exact success rates, however, at 75/70, its pretty obviously not worth it, and while it would be worth it if the sucess rates are higher then that (although I don't think they are), I don't think they made it the optimal grinding way for any items.
That said, I suppose its not really that bad if you only need 12, just a little bit sub-optimal.
And don't even bother trying to use it to grind for antique mysteries, using casing to get them is a far better return.
On which note, if you have a gang of hoodlums, using casing to get teir 3's and converting them to teir 4 items, is pretty handily the best echo return in the game.