The 22-23 senders are different from all other electrical senders Packard used because they are bimetal instead of resistance. The bimetal type uses a heater to make the bimetal strip perform an on/off action with a set of contacts rather than send out a straight changing resistance value. How long or how quickly the on/off cycle happens is determined by the float moving a cam to change pressure on the strip to determine how quickly the heater can cause the bimetal to open the contacts. The gauge follows along with its heater and bimetal strip moving the needle farther and farther depending on the time the sender contact is in the on vs off position.
One person who also had a rusted and unrepairable sender has been working on finding a replacement for the 22-23 series senders and may have come up with something. If you haven't been following the PAC forum
http://www.packardclub.org/forum/ check out the Project Blogs and specifically the
49 Packard 8 club sedan blog by Tinman_70. On page 46 of his restoration check out some of what he has come up with. While he has changed the fuel tank, he did some early work with different senders and adapters which would fit the Packard tank.
If you haven't posted there before do the necessary stuff so you can log in and then send him a private message and see if he can give you a current status of his progress. If he has found a reasonable Ford bimetal which would be an alternative to the original with the same on/off working, that is great. Issue for a blanket replacement would be the float arm length because Packard did use two different capacity tanks with different arm length senders. On his earlier work mentioned in some of the early pages of the blog he used a constant resistance aftermarket sender and an adapter to mount it. I don't know how well that worked out since the gauge does not get the cooling off period between on and off cycles in the sender.
Since you are both in the same predicament maybe you can swap ideas.
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