Even though I clamped and cauled the top and shelf during the glue up there was still a slight offset between the panels, maybe around a 64th or so, maybe a little less.
I machine planed the panels before the glue up so the panels were pretty flat and reasonably smooth.
I like the tactile quality of a planed surface more so than a sanded surface so the offset and the desired for a planed finish combined to lead me to hand plane the finished top.
Hand planing the top turned out to be a bigger hassle than I anticipated. There was a low spot in the middle along the glue line so more planing was required than I hoped for going in. The grain reverses in multiple places so tear out was a problem. I ended up planing mostly cross grain with a jack to flatten the panel. I followed up with a smoother using a 50 degree blade (pretty high angle) and the smallest mouth opening / cut I could make. I tried heavier cuts and lower angle blades but I would get tear out every time. That was with freshly honed blades sharp enough to shave with.
The result of the high angle blade and the infinitesimal cuts was a surface smooth as glass with no tear out but it took a LOT of passes. I mean a LOT. Here’s one pile of shavings from smoothing one side. You could pick pretty much any one of these shaving and see through it, they were all that fine. I made about three piles of shavings like this and didn’t reduce the thickness of the top or shelf by more than a 32nd. These were a pile of wispy shavings.
Here’s how the shelf looked almost done. You can still see some of the plane marks but most of the tear out was cleaned up by now.
Here’s the top finished.