The resistors are there to ohms match the low impedance injectors to the ECU injector drivers.

If a resistor is bad it usually creates an open circuit and the corresponding injector won't open.

A stuck injector can either be mechanical (e.g. pintle stuck) or electrical. If an injector driver was bad it would affect other injectors since it's batch fire.

It is simple to diagnose. Disconnect power to the injectors and coil and crank. Pull plugs, if all cylinders are dry except #3, then #3 is mechanically stuck. If all are dry, there still could be a trigger issue. They could swap injector plugs to see if they can get a different cylinder to act like the problem one. Since it's batch fire swapping them for diagnostics isn't a big deal.

This whole thing seems silly to me. With the proper tools, knowledge, and a standard "flow chart" this shouldn't take more than a few hours to diagnose. These van, though they look weird, are still regular internal combustion 80's EFI vehicles. There are no flux capacitors, and it isn't powered by a Mr fusion.

I really do wish you luck.