duplicate

Forget the ground strap or ground system. The only thing that would happen if it was somewhat compromised is the glow plugs will not heat up as much.

What caught my attention was the random substitution of used glow plugs to replace failed plugs. Your random failing plugs may be because of actual differences in resistance in various plugs. Since all the plugs are in parallel. Total current flow through one plug is determined by its actual resistance.

Inefficiencies usually eliminate any one given plug really heating up to it's maximum temperature. Yet with plugs of different resistances you may be increasing the efficiency and allowing a couple of plugs to reach their actual rated current flow. This is higher than they have been pre conditioned to so they fail. Either get five good plugs from the same engine and test them for about the same static resistance and install them. Or buy a new set in a reliable brand name.
Another possibility is the relay is coming back on sporadically. I know you changed relays yet this could be an external to the relay defect turning it on. I would consider driving with a digital meter or 12 v bulb wired to a glow plug but extending back into the car to eliminate that as a possibility for a period of time.

The problem starting when you changed out the battery is logical. More voltage than the old plugs were conditioned to was made available. Probably had a poor battery for quite awhile.

Also check the battery charging voltage with engine running. You do not want to see more than 14.8 volts or the regulator in the alternator is bad.

At least you really cannot lose glow plugs left and right. They are all on the same side of the engine.