Can too much ridge ventilation be detrimental?
With the solar-powered vent and two static vents being so close together, I wouldn't be surprised if the the solar-powered vent (because it's powered) is pulling most of it's air from the two static vents. You might be able to check this by using toilet tissue, feather, incense smoke or something to determine air-flow direction through the static vents while the solar-powered vent is running.

If the net effect is that air is being pulled in, then none of those vents are doing as much as they should to cool the attic. Some of the air through the soffit vents is being exhausted through the solar-power vent, to be sure, but the static vents aren't helping.

If I were going to make changes, I would consider the following, in order of preference...


Remove and seal up the two static vents. This alone would cause the solar-powered vent intake to come completely from the soffits and thus pull hot air out of the entire attic area underneath.
Remove the solar-powered vent and install a ridge vent the entire length of the ridge next to it. As this makes venting totally passive, it might not be enough for your climate. Depending on size and efficiency, the solar-powered vent without the static vents may move more air. If still not enough, I would think more CFMs of air could be vented using a line-powered unit, but haven't researched it.