A few more thoughts then on the films:
May I suggest some urgency? I went to the State Library of QLD on Sunday, and was told that some of the films had degraded (in a toxic sense) and been withdrawn - so I can't continue searching until I go next to the Mitchell or National libraries - hopefully they are still in service.
As for finding what you want on the films, first use the finding aid (it's online too, as well as being a booklet in libraries) to check the War Office reel and piece number to start from. Forward though the reel until you get to the correct piece number on the right side. Once you get there, it is less tiring if you skim until you come to the page labelled 'sergeants'. There will be one or two pages per pay quarter. Read across the page and it should tell you how much money per day, over what period (eg 90 days), whether the soldier had earned a increase and the location of the soldier.
With respect to the private I am researching, I had a non-effective date, so I elected to research the last film first (see my previous post about the genie-details I got by doing that). You will get that benefit too once you can access the regimental record at the (UK) National Archives. There is a page or two at the end of each quarter detailing soldiers who are non-effective, died, discharged, transferred. Such a shame your sergeant survived Tasmania (and India?) only to die on the voyage back to Britain - but there might therefore be information on him in the ship surgeon's log.
I assume your sergeant's children had relatives to take them in: lucky hmm. I am no expert on the subject of British military pensions, but I believe the system supported the soldier himself not his family.
It is very tiring work - and from what library staff have told me, there are no plans to re-film. I wish you luck in your search here and at Kew. If you do go to Kew, maybe a search will given you a physical description - wouldn't that be something!
Lexia