what about a rich eccentric? A roman sir Richard Branson, that just must know what lay beyond the horizon.
and searches for the shipbuilding techniques he needs and finds the Venetii / phoenician designs etc
There is no secret lost technology about the Venetic ships. Their shipbuilding techniques continued into the Roman period and were combined with those of other cultures. If you wanted a ship like that, you could have it on the open market.
The problem with the rich explorer idea is that there were so many other directions open for exploration. It's not that the Romans didn'tr explore or develop new ideas and things (it's a fashionable view that they didn't, largely a backlash against the Gibbonesque 'just like us' story, but it doesn't really hold up that well). The Atlantic is just a remarkably uninviting prospect for this. Why go out into a dangerous, unknown, cold and largely empty sea if you can look for things like the source of the Nile (tried and failed under Nero), the overland route to China (tried and probably succeeded, though not opened for regular trade until later), the trans-Sahara caravan route (tried, outcome uncertain) or the sea route to India (tried and succeeded even before Roman rule).
I think your prospects are better if you put something out there first. If a reason exists - a merchant ship blown off course, the chance discoovery of the Azores or Canaries, trade down the African coast or a freak voyage all the way across and back), it's fairly rational to go look. If not - why on earth should you? Columbus' momentous error is hard to replicate here because any Roman who believes that the Earth is a sphere will also have learned of its correct size (calculated remarkably precisely) and have a reasonable idea of the distance to India, so he'd know there is no way you can reach China by heading West.