You can use your router table as a jointer to give you a perfect, straight edge. You need a split fence. You place spacers behind the outfeed side of the fence and line that up with the edge of your bit. Difference should be maybe 1/16th inch farther forward than the infeed side. Cut your pieces slightly proud so your dimensions are correct after jointing.
Also, the blade you're using in the saw leaving a rough edge or saw marks. I suggest you get a new, GlueLine blade from Freud. It's a rip blade but it gives an extraordinary smooth cut edge. If you want to perfect it, you use a little sandpaper wrapped around a block. Make long, full length strokes. I almost never use anything finer than 220 grit sandpaper for such tasks. It can also be smoothed with a hand plane.
Here's the blade:This is the premium (industrial, full kerf version, which has extra heavy tips so you can get it sharpened many times more than the consumer (red) version. It also cuts a flat bottom so you can use it for splines.
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Personally, I think the sander is a bad choice for this task because as you move it back and forth, the center gets more sanding than the ends, giving you the gap you mentioned. One last detail. Pop for a Wixey digital angle gauge and set your blade to precisely 90 to the table. For glueups, that makes a huge difference. With that blade, I don't have to sand for glueup panels.