Over the weekend, I finally caught back up with Shiloh again on
Ultimate General: Civil War, this time with a better corps (though still only 15 brigades instead of 20 -- but the game assumes some of those twenty will be dedicated skirm companies and cannon batteries, both of which I'm ignoring.)
I can confirm that having captured the flag on day one, there is no "Finish the mission" button, ever. The mission drags out to the absolute end of the day. I
did win this time, but I suffered some rather harsh casualties to my irreplaceable superweapons (the Lorenz and MJG brigades), because I got impatient at not being able to 'finish' and just set brigades in groups to push the yankees around the map and off their attempts at retaking Pittsburg Landing. By the end, I had gotten all but a scattered handful trapped in a corner of the map, constantly being shot and meleed. The after-tally couldn't accept that I had kicked sooooo much butt, and just straight lied about how I had caused (only) 50ish percent casualties. Not worth the irreplaceable super-weapons.
I will probably go back later this week and replay the final push (when the total map opens up at last for both sides of the fight), with an eye toward doing better fieldwork to protect my precious quality rifles while maneuvering around better to get inside the picket line and stay there defending the Yankee's own base against Yankee aggression.

If I can get out with fewer casualties, I'll be a lot happier: having experimented to the limit, I understand the game just doesn't expect me to win on day one and has no code to understand it.