Foundation replacement

Thanks everybody who responded to my inquiry about 'jack posts'. I did purchase three at HD, they are available by mail only.
The foundation that is perpendicular to the floor joists is kind of a no-brainer to replace. I went inside a couple of feet, placed a beam to hold up the floor joists, knocked out the small concrete stem wall, replaced the sills, and will be pouring a new footing with concrete wall replacement stem wall. Of course this is after a lot of digging. I can now get my small Kubota underneath the house.
HELP!! The solution for the foundation parallel to the floor joists has me puzzled. Do I simply support the last floor joist and allow the last 24 inches of the house to hang. (Joists are on 24" centers). Do I do this in, say, 6 foot bites? The two old plates on the concrete footing along with the rim-joist that sits thereon, are too damn rotten to place a jack under. I could remove a foot or so, place a short horizontal 4x4 and jack against that.
Any ideas to streamline this would be appreciated. I have about 40 feet to replace and would rather not do it in short 3-4 foot sections. My concern is that I would like to place rebar in both the new footing and stem wall, and of course continuous rebar etc. would be a lot stronger, plus, I can call out the cement truck and pumper just one time.
Thanks for all replies, Ivan Vegvary
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