Yes exactly Wilco. Technically it's called a concrete-encased electrode. The best results from any grounding electrode are from an electrode that is installed in soil that remains as consistently moist and as physically stable as possible. You want to keep your grounding conductor as short as possible. At the same time you want to keep it away from any other grounding electrodes in the Earth. If you have some in a good location that are not working well you could consider disconnecting them and installing others that are more conductive. And why are your electrodes only 2 ft long. That does not meet NEC requirements.
Before I went to the expense of x-raying and chipping my Foundation footer, I might try ditching the gem potting compound and driving some rods at an angle. You can rent a macho V, 35 or heavier -pound chipping hammer with a ground rod cup from most rental places for $50 to $70 a day. Two people using one of those tools can slam a couple rods into the Earth in minutes. Use the 5/8" copper Rod. The 3/4 " 10ft rods are a bear to drive.
You could also rent a Ditch Witch and lay a deep Trench in half an hour with one of those. I would go as deep as I possibly could. You want to be where the Earth remains moist. After dropping the rods you want to continually Tamp the dirt down as you cover the rods.
Try to avoid any locations that contain sandy soil. Sand is a horrible conductor. You want firm clay like, organic type of soil. Not too black and soft. Light brown or red that's somewhat tacky.'
If none of that is available and you can't drive a rod at least 3 feet deep on angle, then I would start considering the concrete encased electrode option. I noted earlier how you can feel a rod bite. It will shoot right through the first few feet of Earth, then it will go consistent and slow. That is the biting phase. If you never hit that and it just drops through the earth, then bottom out on a rock, you're not getting a good ground. If it drives slow for 4 or 5 ft then bottoms out, cut it off and use that conductor. It's probably pretty good. Technically it's illegal to cut it off but you're in a tight spot and you're throwing supplemental grounds in.
By the way, what is your cold water line. If it's a galvanized or copper pipe why don't you just bring a superior grounding conductor from your panel to it.
I don't know the age of your house, but a cast iron drain pipe is also an excellent grounding electrode you should look for.
A steel well casing is also an excellent grounding electrode.
You can also consider a irrigation system on a moisture meter that always keeps the moisture around your grounding electrode slightly damp.
