So, it was an epic battle! I took the advice from earlier and landed at the capital. The flower wasn't there! Fortunately, it was near the adjacent city so I didn't have far to go. Hutama, who built the flower, had an entire mini-continent to himself the whole game so he was easily in the lead score-wise. It took me nearly 15 turns to get an army into position outside his borders (We're just passing through... I swear!) During that time I made every trade I could manage with the other civs in exchange for favors.
D-Day came and I traded in all my favors for declarations of war across the board. I moved in a handful of arbiters and some shepherds loaded with aircraft and started bombarding the flower. Behind them came my Invasion force of Prophets. What do I see heading for me but a group of about a dozen Poseidons!
It takes about 3 volleys each from my ships to down one of his, and I'm losing units 5 to 6 per turn. To make matters worse, he's garrisoned artillery units in the 2 cities flanking the flower. My troops are sacrificial lambs at this point, hitting the shore for no reason other than to take hits from the artillery and buy time for my strike force. My units are barely making headway and I'm down to a single turn before he declares victory.
On my last round my flanking prophets are down and I have a single land unit in range of the flower. I use all my fighters to bombard it down and check my combat odds. Civ tells me the attack is a stalemate. I've got no choice... this is my last turn to try to stop the victory so I move in... and down the flower! The next round the last of my invasion force is destroyed and I pull whatever I can back.
I walked away with 2 Arbiters, 1 Shepherd, 2 aircraft and a prophet... all of them near death. Just made it into allied space before his navy caught up with me. About 5 turns later he demanded peace and about 20 turns after that I won by contact victory.
I know BE has some patching to do, but so far I'm enjoying it