If you install ridge vents without adequate soffit venting the stacking effect of the rising hot air will suck the air through leaks in the ceiling and walls, not only the attic. This would make your house hotter in the summer and colder in the winter and end up quite a bit less efficient. It’s important to balance the air going into the attic (soffit) with the air going out ( ridge or gable vents). Barring that it would be better to just install additional vents in the other gables. You should avoid vents that penetrate the roof plain since snow/ ice can build up above them due to heat loss and the melting can refreeze near the eaves. Once again there is a formula for the size of vents for the square footage of the attic. Your building department could help you with that.
As you said, ridge vents work great, to be fair you did recommend soffit venting along with the ridge vent. OP didn’t think he could do a soffit vent in his situation. Doesn’t mean he couldn’t just that he was looking for a workaround ( my interpretation anyway). I was really thinking of helping others understand the dynamics involved with attic venting. The makeup air has to come from somewhere and it would be bad for it to come from the conditioned space ( the living space). Most people have no idea how leaky their houses are
