“Should” versus “would”
On the other hand I think I could… reform & become quite strict about not getting drunk and I am pretty sure I should be faithful.
Emphasis mine, of course. Now, when I read this, given its context in the rest of the letter and having seen and read films and plays from the period, I am confident in interpreting it not as meaning I'm pretty sure that it would be right for me to be faithful, but rather I'm pretty sure that I can be/will be faithful. In today's English it is very unusual to see the word should used in this way; the word would might be used with the same or very similar meaning as should has in the above quote.
Oxford Dictionaries Online gives a compatible meaning for the third definition of should:
3, formal expressing the conditional mood:
(in the first person) indicating the consequence of an imagined event:
if I were to obey my first impulse, I should spend my days writing letters
referring to a possible event or situation:
if you should change your mind, I’ll be at the hotel should anyone arrive late, admission is likely to be refused
Any interesting thoughts or information on the history of the word would be appreciated but I imagine that's too open a request to be valid as the primary question, so I'll ask over what period was this use of should common?