I think this would fit... Having just replaced it, the battery tray is a little weird, but there is a padded 'blanket' that goes around the battery. I put it back on, but it seemed rather pointless and I think without it, the extra 3/8" would be available.
I am not sure why you are worried about not reaching a full charge. When ''running' the battery is the usual 14.4V, and the specs on the Weize you found say "Charge Voltage 14.4".
The terminal orientation is reversed, but you would need to adapt the terminals anyway because the Weize does not have the big 'lugs'.
Heck - If I hadn't already replaced the battery before seeing your post, I may have tried one of these !
But I am now having second thoughts about my battery capacity guestimate because of this -
We also have a 2023 Tesla. Tesla now uses a Lithium Ion battery for the low voltage systems. Hopefully it will last a long time, but it is quite expensive if it fails (I think around $800). Of course, it is only available from Tesla, and it is not simply a 2-pin device (there are other connections, precluding the use of a generic battery). In addition, it is nominally 15.5V, but rated at only
6.9 Ah. This causes some issues like the auxiliary power outlets have 15.5V which could damage electronics that you might plug in. You certainly have to be mindful of this or risk damaging something. It is a little hard to believe that the Tesla is OK with a measily 6.9 Ah battery and the Clarity needs so much more. Of course, I am not certain whether the Tesla can invoke the HV battery to charge the 15.5V one when the vehicle is off. Many unknowns there...
The Tesla battery looks like this:
It would be tempting to just try something like this:
https://a.co/d/cXS65Yi as an experiment. The 18 Ah version is $52. If my 100 mA parasitic current is right, then this would only last around a week in the Clarity without driving.