I did a quick test with my idea, and much the same without whipping another worker.
First whip out worker:
Turn 56 chop forest, T 57-63 road from Antium to river like Stochastic says.
T 58 put worker on build, 7 turns build, 3 turns for max overflow of 39 hammers on 2 pop whip.
T61 whip worker
T62 worker 2 chops plains hill, micro'd Rome to put one pop on mined hill.
T64 worker 1 helps out after fininshing road.
T66 forest chopped
T67 TGW!
Results: We have 2 workers now Antium is connected, with a warrior. Sailing is researched (didn't do anything except test TGW), Rome is at 2 pop. 2 forests chopped.
Test 2:
T56 Worker moves to make road to Antium from river, done T62
T62 Rome has stone TGW in 8turns.
T64 worker back to chop pre-chopped forest, TGW 2 turns.
T65 Rome goes to 5 pop, unhappy.
T66 TGW!
Results: TGW is one turn quicker, Rome has 5 pop, better for whipping, one forest chop needed, one worker. We can build settler in nine turns, or worker in 7 (whip unhappiness). Sailing in next turn.
In both tests a barb archer was chasing Hammy's bowman around the flood-plains, so TGW needed.
On the two tests done I like result 2 better, gives us TGW one turn earlier, and allows us to whip in 2 turns.
On tech we need to research pottery before writing, so Sailing is not a terrible idea, whip out a settler, build lighthouse, start TGL, and in the mean-time research to writing, through pottery.
So for my last 4 turns I propose whipping the settler, sending him up to the desert hill no.2, with the warrior from Antium providing cover on the way. I'll start a lighthouse in Rome, and have a worker building in Antium from t63.
Cross-post with Stochastic, yes a 25 minute post.