Maybe you could build your own, with the open-source
TMK firmware and hack it, just downgrading the USB version in the
device descriptor.
That firmware I linked is for the ATmega32u4 microcontroller, which is found in the Teensy 2.0 and Arduino Pro Micro.
There should be no difference between USB 1.1 and later protocols when it comes to the HID class protocol, which is used for keyboards.
However, I have not been able to find any good description of what the differences are between USB 1.0 and USB 1.1, or if there are any versions of HID below 1.11 but the latter might not matter.
I suspect that the 1.1 revision could be mostly about compliance to a better defined set of the same specifications. I have found conflicting information about the highest speed of USB 1.0: if it supports "Full Speed" (12 Mb/s) or not. Maybe "Full Speed" was considered an extension in USB 1.0 and compulsory in 1.1.
I think the firmware I linked to does not support anything else than Full Speed but I know the microcontroller itself supports low speed, so maybe that could be hacked as well but I think it is plausible that that is not necessary.