Replacement gas burner assembly
For your 70s lady Kenmore dryer, is part number 279894, the wiring harness may not match up perfectly. You can just splice the two wires.
Changing the igniter will not do any good the igniter resistance does not react with the valve coils it has nothing to do with the resistance of the igniter. As long as the igniter gets nice and hot as yours is doing it is fine.
Once the igniter gets hot and it cycles off, the power goes to the secondary gas valve coil which is what has failed on your dryer.
John