I’m not sure what you mean by: “The smaller roof vent for the small bathroom that’s getting the smell”. Is that a roof / attic vent that the small bathroom’s exhaust fan is connected to? Is there an exhaust fan in that bathroom at all? If so, does it discharge into the attic / close to the roof vent, or through the roof / how close is this discharge point from the vent stack pipe and the electric vent, does the bathroom exhaust have a functional damper?.
I don’t see how the electric dryer can be responsible for the sewer gas odor in that small bathroom. The only thing I can think of is that the dryer (that needs so called make-up air while running) or / and the electric attic fan depressurize your home causing imbalance in the sewer system.
Somehow, the sewer gasses discharging from the vent stack (assuming there’s no cracked sewer / vent pipes (maybe in the attic, hidden under insulation), or faulty drain trap) find their way back into the bathroom.
Maybe through an open window (probably not), bathroom’s exhaust fan (possible), or some other way... I’m assuming that you cannot pinpoint the source /area of the bathroom that this odor is originating from.
Well, I would turn off the electric fan in your attic and repeat the dryer’s cycle, see if that changes anything. If you have that exhaust fan in your bathroom, seal it off with a piece of plastic and run the dryer. Maybe based on that information you’ll be able to narrow your investigation.
Please let me know, click “comment” below if you have more questions.