Issues with jailbreaking my Kindle 3rd gen

[Greta19]

Hi all,
I have a Kindle Keyboard 3rd gen, model D00901, serial B008A0A003555E2C, running firmware 3.4.2 (build 2687240004). WiFi-only unit, ad-supported.
I've tried every software jailbreak method I can find and nothing works:

Update_jailbreak_0.13.N_k3w_install.bin → U007 error
Update_jailbreak_0.13.N_k3w-3.0-to-3.2_install.bin → U004 error
Update_jailbreak_0.5.1_k3w_install.bin → Error 3
KindleBreak browser exploit → browser blocks file:// protocol entirely
SSH over USB → port 22 times out (stock firmware)

I've read the build script comments noting U007 is expected on FW >= 3.1 through the normal update mechanism. I also see the build script covers 3.2.1-3.4 but my device is 3.4.2.
Is there any known method for this specific firmware version? Has anyone successfully jailbroken a K3W on 3.4.2?