Need help connecting points after using mirror tool

Josh, after seeing all your screenshots, and with Smart Guides on:

What happens if you:

1) Select all the left side artwork;

2) Object>Transform>Reflect (Vertical axis, as the default) as a Copy;

While everything is still selected:

3) ShiftClickDrag (hold Shift and ClickDrag) the whole copy set to the right by one of the leftmost end Anchor Points (that are to coincide with the original rightmost counterparts) until it snaps to its original rightmost counterpart (Smart Guides say anchor if all goes well);

4) Deselect (click an empty spot on the Artboard), then ClickDrag over each set of counterpart Anchor Points and press Ctrl/Cmd+J for joining?

Josh,

I believe Bobby has given the answer (the artwork shown could also be the outcome of the good old Effect>Distort&Transform>Transform>Reflect X with one of the leftmost Reference Points chosen).

With regard to the "They barely look like they are overlapping each other", it seems to me that you have an (almost completely) accurate fit, and the funny way the open ends meet just reflect your using Butt Cap along with Miter Join; with Round Cap they will look more assuring, but no need to change because they will become Miter Joins when Joined (if they are fit accurately/coincide).

If you are using a live effect, such as the Repeat Mirror effect or something from a third party plugin (Astute Graphics' Mirror Me plugin) the effect needs to be "expanded." The paths also should be on the same layer so they can be combined into compound paths. When the two halves of the paths are compounded together the central portion where the slight overlaps or gaps are occuring can be joined.

You could try the Join tool (the one from the tool panel, not the Join command from the Object menu)

You will need to join the path at each of the reflection points by using the Direct Select tool. Drag a box around the points so both are selected and then use Cmd(Ctrl)-J to join.