Maybe this is an engine performance problem and is not related to the wheels, suspension, or drive train at all.
Weak fuel pump, clogged fuel filter, partially clogged catalytic converter, weak cylinder due to low compression, etc, etc.
As to CV joints, checking them while they're installed in the car is not always a reliable method. It's entirely possible for joints to feel perfectly tight with no slop at all but they may have odd wear patterns in the bearing races that can cause binding. This binding can cause a shimmy.
The only reliable way of checking them is by removal and checking them on the workbench; providing one knows what to look for.
Of course if you're going as far as removal then you might as well replace them.