GSF car parts show the Yuasa YXB 5054 as compatible with the mk4 Jazz HEV . £65.09 ( which may include delivery)
https://www.gsfcarparts.com/products/ybx5000-silver-high-performance-smf-battery-5-year-warranty-za042670https://www.yuasa.com/uk/ybx5054At first glance this does seem a closer match in physical size than the YBX3202 or YBX5202.
However the Yuasa site shows it as being ca/ca -ie calcium terminals. Although this has many advantages I believe calcium batteries are more vulnerable to permanent damage if allowed to deeply discharge more than 3-4 times. And also need a compatible trickle charger to charge them above 80%. (Good smart chargers are compatible) .
The specification given by Honda for the 44b19L makes no mention of it being calcium. But is this just an omission and the battery is in fact Calcium type, which might explain why some people have had problems? But as the Panasonic/yuasa 44b19L appears to be exclusive to Honda models maybe its specifically avoids calcium to avoid this problem .

If so its not been completely successful

I have no figures to back it up but have the impression that early Mk 4's ,which used a different brand of OE battery ,seemed to be more vulnerable than later cars with Panasonic batteries. Even when they too were quite new. So maybe they were improved. But is this enough of an advantage to pay £177 for a replacement? I think I would take my chances with a £65 one rather than pay £177

But might regret doing so if it leaves me stranded

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