Uh, yea, I would also. That’s why I asked the ELECTRICAL INSPECTOR, who directed me to the NEC, which is not overly clear in the supplemental grounding electrode when using the plates. And not very easy to even find online without a paid subscription, so I thought I would pose the question here for some knowledgeable clarification.
You can register for free to the NFPA web site and access electronic versions of the NEC. Just click on the Free Access button searching for NFPA 70. Hit the table of contents button, select Article 250, navigate to section 53 and you're there.
If you buy a hard copy of the NEC, you'll get more illustrations and explanations of things than what's found in the electronic copy. You may get the extra illustrations and explanations if you pay the subscription, but I just own a 2017 NEC hard copy and use free access to check the NEC 2020 version.
You're probably better off trenching two ground rods 30" if you're soil is impenetrable and depths less than 8'. The way I read it 250.53 (4), it looks like vertical is preferred, but if that doesn't work, you try 45 deg, and if that doesn't work, you can bury ground rods horizontally 30" deep.
With just a quick search, 250.52 (7) covers plate electrodes
(7) Plate Electrodes. Each plate electrode shall expose not less than 0.186 m^2 (2 ft^2) of surface to exterior soil. Electrodes of bare or electrically conductive coated iron or steel plates shall be at least 6.4 mm (1/4 in.) in thickness. Solid uncoated electrodes of non-ferrous metal shall be at least 1.5mm (0.06 in.) in thickness.
250.53 Grounding Electrode System Installation.
(A) Rod, Pipe and Plate Electrodes. Rod, pipe, and plate electrodes shall meet the requirements of 250.53 (A)(1) through (A)(3).
(1) Below Permanent Moisture Level. If practicable, rod, pipe and plate electrodes shall be embedded below permanent moisture level. Rod, pipe, and plate electrodes shall be free from non-conductive coatings such as paint or enamel.
(2) Supplemental Electrode Required. A single rod, pipe, or plate electrode shall be supplemented by an additional electrode of a type specified in 250.52(A)(2) through (A)(8). The supplemental electrode shall be permitted to be bonded to one of the following:
(1) Rod, pipe, or plate electrode
(2) Grounding electrode conductor
(3) Grounded service-entrance conductor
(4) Nonflexible grounded service raceway
(5) Any grounded service enclosure
Exception: If a single rod, pipe, or plate grounding electrode has a resistance to earth of 25 ohms or less, the supplemental electrode shall not be required.
(3) Supplemental Electrode. If multiple rod, pipe, or plate electrodes are installed to meet the requirements of this section, they shall not be less than 1.8m (6ft) apart.
250.53 (5) Plate Electrode. Plate electrodes shall be installed not less than 750mm (30in.) below the surface of the earth.
250.52 Grounding Electrodes
(A)(2) Metal In-ground Support Structure.
(A)(3) Concrete-Encased Electrode
(A)(4) Ground Ring
(A)(5) Rod and Pipe Electrodes
(A)(6) Other Listed Electrodes
(A)(7) Plate Electrodes
(A)(8) Other Local Metal Underground Systems or Structures
250.52 (B)(2) shows that Aluminum is not permitted for use as grounding electrode.
If you just install one plate electrode, you'll probably have to get the resistance measured using the "fall of potential" method which requires a tester, and experience to know how to use it. From my limited reading up on it, it appears that other buried metal can affect the measurement, so depending on your surroundings, it may be difficult to make an accurate measurement. It's possible the AHJ may want a licensed professional to make the measurement.
At the end of the day, you're probably better off to have two grounding electrodes installed. As far as I can tell, you can mix and match, so you can have two ground rods buried 30" deep 6 feet apart, a grounding plate and a rod, or two grounding plates. It seems like one option is that you can make a trench 30 in. deep 22 ft long, put both ground rods horizontal, and have a bonding jumper 6ft long that connects the two, then from one electrode go to your subpanel. Alternatively, you can have two grounding plates 6 ft apart, but I don't know if your electrode bonding jumper needs to be 30" deep as well, or if you can use a shallow trench to bond them. It'll be up to your AHJ probably.