Digesting all of the comments and answers above, I borrowed a Hitachi H45FRV hammer-driver from a friend. It took at least 30 min of driving, possibly an hour, spread over six hours, to drive each of two 5/8"rods.
I first started a hole with a custom "willow tree planting" bit, similar to a concrete breaker only longer (~3 ft long, 3/4" dia, pointed tip). The main reasons for that were to get a hole which would funnel water deeper, and get the top of the rod low enough it was more easily reachable. The rods are in the trench at one side, about 8" from the conduit.
I then started a hose and filled the hole and a surrounding puddle to keep a reservoir of water available to drain into the hole and down the side of the rod. It took 5-10 min to drive a rod 1.5 - 2 feet, at which point 2-4 min of solid driving got no-where. I alternated 2-4 min of driving from one rod to the other about 3 times. With no success, I left the hose dribbling into one of the puddles and did something else for a while (30 min to 1hr). I then tried again, but another 5-8 minutes of driving in 2-4 min sessions alternating between rods made no further progress. I left the hose dribbling...
After another couple of hours I tried again and was able to go down another 3 feet or so. Hammer more, keep the hole filled with water, wait a few hours, and eventually I got both rods in.
I don't know how the Hitachi compares to a Hilti SMS Max mentioned in this post; but it's what I had available.
I didn't have a proper ground-rod driving bit, and I couldn't find one in the nearest (65 mi away) "metropolis". But the Hitachi head has a 3" or so deep collar that engages the bit. The bits have a flat spot in which a locking pin sits to keep them from sliding out when the driver is pointing down. You pull back a knob to retract the locking pin; turning the knob leaves the pin retracted. The bits are 3/4", so a ground rod fits in the bit-hole fairly well, and with the locking pin retracted, it's a pretty good arrangement.