What makes some commercial JFETs asymmetric?
Many JFETs are symmetric and this is sometimes indicated in the datasheet such as the

Source: https://shop.micross.com/pdf/LSM_2N4117A_TO-71.pdf
If it is indicated then you know its symmetric otherwise you would have to assume either.
I think this is question is backwards:

What about its physical construction makes this JFET, and others like
it, asymmetric? Why can Vgd be so much higher than Vgs?

If there is asymmetry you can infer this from measurements or from the datasheet because if the physical construction were symmetrical there would be no difference.
A better question would be: Can I infer that a JFET is asymmetric if there is a difference between Vgd than Vgs. I believe the answer is yes, but you could never be sure unless you actually check the physical construction or a patent. Also if there were Cgd and Cgs listed and they were different I also think you could assume asymmetry.
This J308 &quot;N-Channel JFET&quot; has a different Cgd and Cgs.

Source: https://www.digchip.com/datasheets/parts/datasheet/078/J308-pdf.php