These look like Origo instructions, and I agree it looks like this stove follows approach with the red areas mounted to the side of the cabinets and the pivot point above the stove.
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I suppose an alternate to this approach would be to do like this and remove these bracket arms and just use the pivot bolt (if I can source it) & small bracket approach that most Force 10's use. This would keep the stove more flush with the top of the countertop which I prefer.
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I'm not following quite how you are planning to do this. It sounds like you are moving the pivot location, that would change the ability for the stone to gimbal.
It looks like you need to find a fixation method at the connection points on the arms where you have the red dots on that arm. Are there any more bits that came with that stove not shown in your pictures?
It looks like those arms are meant to be fixed through those three holes. How to fix them is the dilemma. How to access those fixation points while mounting or removing the stove seems to be a question.
Some things come to mind:
1) put something like a carriage bolt in them with the heads sticking out and make a bracket they can slide into similar to the bracket you had with the circled tab. Having the three would keep that arm immobile - which you want.
2) Get the arms positioned correctly and simply screw through those holes into the structure where your stove goes. I imagine that's the original intent.
Also, bear in mind those arms could be mounted at any angle. They don't have to be straight down. They could be behind the stove, above the stove, pretty much anywhere. Once those three holes are secured to whatever, your stove will gimbal correctly.
Also bear in mind, you don't need a gimbaled stove. I know a number of sailors that have extensive travels that say that a fixed stove is fine. Some prefer it. Just a FYI.
dj
