I'd need to check the actual content of the VV package (it used to be a data.tgz/data.stgz last time I checked, but that was a loooooong time ago), but, thinking about it, if it is actually a full update, and not just a delivery mechanics for another type of payload, we can't re-sign it, because we can only steer the OTA updater into accepting our packages, not the initrd one.
EDIT: Morning brain (it's 4PM, I know.

). A full update for additonal files doesn't make any sense. So of course it's still a data.stgz

.
Which means.... that I have no idea how data.stgz files are handled on current FW

.
But it may be as simple as either dropping said payload, extracted via KindleTool, manually into the userstore and rebooting. Or if that doesn't work because the update checker also has something against data.stgz, just unwrap that again with KindleTool, and drop the VV voice data in the right place (probably the userstore, IIRC), reboot, and be done with it?
Roughly following from @knc1's previous convert command (actual tarball decompression done via GUI, which explains the missing steps and extra subdirectory):
Code:
tar tvzf update_voice_kindle_all_new_oasis_converted.tar.gz ──(Fri, May 18)─┘
-rw-r--r-- signdaemon3/signdaemon3 69 2018-05-15 20:41 update-payload.dat
-rw-rw-r-- signdaemon3/signdaemon3 136226164 2018-05-15 21:27 data.stgz
-rw-rw-rw- signdaemon3/signdaemon3 256 2018-05-15 21:27 data.stgz.sig
-rw-rw-rw- signdaemon3/signdaemon3 256 2018-05-15 21:27 update-payload.dat.sig
kindletool convert -k update_voice_kindle_all_new_oasis_converted/data.stgz ──(Fri, May 18)─┘
Converting userdata package 'update_voice_kindle_all_new_oasis_converted/data.stgz' to 'update_voice_kindle_all_new_oasis_converted/data_converted.tar.gz' (without sig, keep input).
Bundle SP01 (Signing Envelope)
Cert number 2
Cert file pubprodkey02.pem (Official 2K)
Bundle GZIP (Userdata tarball)
tar tvzf update_voice_kindle_all_new_oasis_converted/data_converted.tar.gz ──(Fri, May 18)─┘
drwxr-xr-x jenkins-official/jenkins 0 2018-05-15 20:08 voice/
-rwxr-xr-x jenkins-official/jenkins 152365343 2018-05-15 19:34 voice/vox_en_us_salli22i
-rwxr-xr-x jenkins-official/jenkins 1980678 2018-05-15 19:34 voice/lang_en_us.dat
TL;DR: That's an awfully complex delivery mechanic just to put two fricking files in the userstore.

.