[Galaxy Note 3 Android Development] zmore:
Heimdall notes

You can use Heimdall too. You'd either use the Heimdall GUI front-end, or the faster commandline, to flash each of the files to their respective partitions.

The important bit is making sure you get the mapping correct between partition name and firmware filename, which is why you always do a print-pit first.

heimdall print-pit > note3.pit.txt

Download and unpack the firmware you're going to use. You can use the smaller tar.md5 that haggertk prepared for your N9005, or download from elsewhere as I did to get the entire FQD2 firmware+ROM for my N900T and only flash the baseband files (so I'm ignoring the system.img.ext4, cache.img.ext4, boot.img, and recovery.img) .

To unpack your tar.md5, you first just need to strip off the md5sum at the end of it:

head -z -n -1 N900BLAH_BLAH_BLAH.tar.md5 > N900BLAH_BLAH_BLAH.tar
tar -xf N900BLAH_BLAH_BLAH.tar

Then check the mapping between those unpacked firmware files and the partitions they want to be flashed to:

$ for i in aboot.mbn modem.bin NON-HLOS.bin rpm.mbn sbl1.mbn sdi.mbn tz.mbn ; do grep -B1 "$i" ../../note3.pit.txt ; done
Partition Name: ABOOT
Flash Filename: aboot.mbn
Partition Name: MODEM
Flash Filename: modem.bin
Partition Name: APNHLOS
Flash Filename: NON-HLOS.bin
Partition Name: RPM
Flash Filename: rpm.mbn
Partition Name: SBL1
Flash Filename: sbl1.mbn
Partition Name: DBI
Flash Filename: sdi.mbn
Partition Name: TZ
Flash Filename: tz.mbn

Then get into download mode manually so it'll stick and craft the heimdall cmdline to flash 'em:

heimdall flash --ABOOT aboot.mbn --MODEM modem.bin --APNHLOS NON-HLOS.bin --RPM rpm.mbn --SBL1 sbl1.mbn --DBI sdi.mbn --TZ tz.mbn

EDIT: Flashed my phone just now using the above cmdline, and all's well after the reboot: still have SIM service (on 6/27, not 7/04 yet), and the "Phone INFO" app shows both my bootloader and baseband version updated to FQD2.

# heimdall detect
Device detected
[root@ivy:0j:639h:0e FQD2]# heimdall flash --ABOOT aboot.mbn --MODEM modem.bin --APNHLOS NON-HLOS.bin --RPM rpm.mbn --SBL1 sbl1.mbn --DBI sdi.mbn --TZ tz.mbn
Heimdall v1.4.2

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Initialising connection...
Detecting device...
Claiming interface...
Setting up interface...

Initialising protocol...
Protocol initialisation successful.

Beginning session...

Some devices may take up to 2 minutes to respond.
Please be patient!

Session begun.

Downloading device's PIT file...
PIT file download successful.

Uploading ABOOT
100%
ABOOT upload successful

Uploading MODEM
100%
MODEM upload successful

Uploading APNHLOS
100%
APNHLOS upload successful

Uploading RPM
100%
RPM upload successful

Uploading SBL1
100%
SBL1 upload successful

Uploading DBI
100%
DBI upload successful

Uploading TZ
100%
TZ upload successful

Ending session...
Rebooting device...
Releasing device interface...

EDIT 2: And after updating to 7/4 hltetmo I finally have SIM service this time thanks to the updated firmware. Woot! :D

This is probably the last time I'll bother to update this old phone's firmware, but it needed it.