I decided to go with 6x6 Ellis screw jacks to match my 6" beams. I also bought pre-cast 16x16x4 solid concrete footer blocks and a 6x6 from HD.
Unfortunately, I hadn't considered that my 3 foot headroom estimation was for me with my head between the joists, so the bottom of the beam was a good bit closer to the ground. As a result, I had to do some excavation to get enough vertical room. Since I was placing these jacks relatively close to the existing piers, I was concerned the excavation would compromise the existing piers, so I bought a length of treated 2x10 and constructed a box to shore the hole.
I had to build the box in the crawlspace due to the small entry hatch. I placed it in location under the beam and dug out the center, using a hammer to move it down by 1" steps. The top 4-5" of soil was very sandy, so there was significant erosion as I dug-- glad I had the box. Ultimately, I did hit well-compacted soil, so I think it was good to do the excavation anyway.
Once I had the hole deep enough, I dropped in the concrete block, a piece of asphalt roof shingle to help spread the load between the steel of the jack and the rough block surface, the jack, and a section of 6x6. I had planned to use an Ellis purlin joiner to create a strong connection between the 6x6 and the joist, but I ran into some excavation issues-- large, live roots that I didn't want to cut-- so I opted to skip the bracket. I believe the roots pre-dated the house as there wasn't evidence of water. In hindsight, the hole would not have needed to be as deep w/o the bracket as I would have only needed an inch or so of exposed 6x6. But, it was easier to dig another few inches rather than re-cut the 6x6.
A few twists of the jack and it was done. I gave it about an extra 1/2-turn using the hammer as a lever, but I don't plan to do any actual jacking. The floor above is level, so this is just for safety.
I've since done one more and it went smoothly as well. It takes about an hour per pier to do the excavation and set up the jack. The biggest work, which I've already done, was getting all of the materials into position. Each block weighs 50+ lbs and each jack 22 lbs. I had to make multiple trips and the furthest pier is almost 40 feet from the closest access hatch. Excavating is tedious but not strenuous.
In any event, both "scary" piers are now shored, so the remaining four are just for completeness. I'm going to be glad once this project is done, but the end is in sight.