That bottom newel post shouldnt have any movement at all. With the additional support of those volute balusters that lower section should be stiff. There really shouldnt be a need for a center post if those balusters are installed properly. Are the balusters loose at the bottoms? Are they nailed at the top? If all this stuff is sound and you still have a lot of lateral movement, then you can put a post in the middle. Here's an idea of what you will need to do and you can decide if you can do it or if you want to hire a pro. Only you can decide, as I do not know your capabilities.
First find the exact center of the rake rail. Now locate the center of the closest baluster to this line. Your post will replace this baluster, just keep you centers in the same spot. If you intend to use a ball top post then draw out your 3" post on the rail. You will need to make these 2 cuts on the rail which will be tough if you need to take down the entire rail without damaging things. If you keep the rail in place then you will need to cut it with a hand saw ( really tough to cut this accurately on pitch). Once the rail is cut you need to notch the post. The best way to do this is to make a half lap on the bottom of the post so that the post will hang down below the tread. You will need to notch out the return so the post will pass through. The post is screwed into the stringer. The depth of the half lap is determined by the offset of the rail. Just keep your centers in line. The rails can the be screwed into the post.
First find the exact center of the rake rail. Now locate the center of the closest baluster to this line. Your post will replace this baluster, just keep you centers in the same spot. If you intend to use a ball top post then draw out your 3" post on the rail. You will need to make these 2 cuts on the rail which will be tough if you need to take down the entire rail without damaging things. If you keep the rail in place then you will need to cut it with a hand saw ( really tough to cut this accurately on pitch). Once the rail is cut you need to notch the post. The best way to do this is to make a half lap on the bottom of the post so that the post will hang down below the tread. You will need to notch out the return so the post will pass through. The post is screwed into the stringer. The depth of the half lap is determined by the offset of the rail. Just keep your centers in line. The rails can the be screwed into the post.