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I'm wondering whether to replace the jack with a manual or another electric.
This is a decision that is more one of personal preference rather than one being a "better" solution than the other. Both my Overlander and Argosy came from the factory with manual jacks. Hitching isn't a particular problem with a manual jack much of the time, but I changed to a power jack on the Overlander three years ago and will do so on the Argosy in the next season or two.
My reasons for preferrring the electric jack relate to my push to make the towing experience as painless as possible. As an asthmatic, the amount of effort required to hitch with the manual jack could trigger an episode and often did in the high humidity of the Mississippi River Valley. With the power jack it is just one push of the button to raise the trailer and back of the tow vehicle such that it is possible to cinch up the weight distribution bars with almost no pressure on the snap-up bracket lever. As a Free Wheeler with asthma, I find my power hitch jack to be an asset that I don't want to be without.
Good luck with your decision!
P.S.: Have you considered having an Airstream technician examine your current jack to see if it is repairable? I have heard of instances where an older power jack can be repaired.