[Transformer TF300T Android Development] pjc21:
Yes I think you should be able use my guide to upgrade from ICS to JB (not 100% sure here)

Short way

you could try flashing the firmwares via twrp,

1st you would need the ICS version of twrp as your on an ICS bootloader, so download twrp-2.5.0.0-tf300t-ICS.blob and copy to your android-sdk/platform-tools folder.

Download both the 10.4.2.9 & 10.4.2.20 firmware zips and unzip to a folder, you should have a second zip file for each - copy both zip files to your microSD.

Reboot to fastboot and flash the ICS version of twrp

fastboot -i 0x0b05 flash recovery twrp-2.5.0.0-tf300t-ICS.blob

Now you can reboot to twrp recovery and flash the 10.4.2.9 zip, reboot and hope all boots up ok - you should now be on stock 10.4.2.9 and will also have stock recovery, you should check your bootloader has upgraded so reboot to bootloader and check the text in the top left of the screen and it should have 10.4.2.9 and also have 4 icons.

Now on a JB bootloader you want the JB version of twrp, so download twrp-2.5.0.0-tf300t-JB.blob and copy to your platform-tools folder and flash via fastboot.

Now you can boot to twrp and flash the 10.4.2.20 zip, reboot, check your bootloader version and flash the JB twrp again.

Now you can boot to twrp and flash the Hydro 7 rom zip, reboot and should be all good

The longer way:

If using the fastboot method to upgrade, download the 10.4.2.9 firmware zip - unzip this to a folder & you should find a second zip file in this folder.

Here I put a copy of the second zip on my micro SD card then back on pc unzip the second zip file (not the copy on microSD card) and you should find a blob file - this is the system blob file for that firmware which is the system, stock recovery, kernel & bootloader all rolled into a one blob file.

Copy this blob file to your android-sdk/platform-tools folder

The version of twrp you need for both 10.4.2.9 & 10.4.2.20 would be 2.5.0.0-tf300t-JB.blob NOT THE -4.2 versions, these are for the 4.2 bootloaders which are firmwares 10.6.1.8 & 10.6.1.15.3

So download twrp-2.5.0.0-tf300t-JB.blob and also put this in android-sdk/platform-tools folder - you can rename it to something shorter if you want, say twrp-2.5.0.0-JB.blob

Now connect tab to pc and boot to fastboot and check that pc can see your device ok

fastboot devices

should see device s/n here, if ok we can flash the system blob we put in the platform-tools folder

fastboot -i 0x0b05 flash system blob

This will take 10ish minutes, it will send file then write file and you should a blue progress bar on tab when it starts to write.

When complete

fastboot reboot-bootloader

You should now check that your bootloader has upgraded, look at the text in the top left of the bootloader screen and make sure it's now has 10.4.2.9 - should have 4 icons RSK (recovery), android (cold boot), usb (fastboot) & wipe-data - don't use the wipe data icon in bootloader - it seems to brick tabs

Here you shoud really be able to just reboot the tab and be fine but I would get stuck at boot animation so next part is a second flash of the same firmware but via recovery instead of fastboot but now your on the bootloader version for that firmware.

So from bootloader screen go to fastboot (usb icon) and flash the twrp recovery, again here you should see a blue progress bar on your tab

fastboot -i 0x0b05 flash recovery twrp-2.5.0.0-JB.blob

When done reboot to bootloader again

fastboot reboot-bootloader

This time select the RSK icon and twrp recovery should boot up. I do a full wipe here in recovery then reboot bootloader and boot back to recovery again.

Now in recovery you can flash the zip file you put on your micro SD, once done reboot system and let it load up to android os.

You are now updated to stock 10.4.2.9 - to get to 10.4.2.20 repeat the process but replace the blob in platform-tools with the one from the 10.4.2.20 firmware. Once done and your on stock 10.4.2.20 you will also have stock recovery so just fastboot flash twrp again, you can then boot to twrp recovery and flash the Hydro 7 rom zip

Sorry for the big post but I hope this helps explain the process, let me know if you need help with any steps