How can I recreate the bottom arch on this text?

Adam,

We had a number of precious threads about vintage text styles, but all those threads were deleted, together with countless other fine old threads, two thirds of all threads up to late 2019 lost.

I am afraid this newer thread is the only one about the ways that were used:

https://community.adobe.com/t5/illustrator-discussions/how-can-i-keep-top-third-of-text-untouched-while-curving-bottom-half/td-p/12186490

This has most probably been drawn like that.

You can also try Astute Graphics plugin Reform text (not free, but maybe you have it already)

You could also try and add a dummy object and then use Bulge: