Radio.
I don't see how radio helps much?
(perhaps a string of line-of-sight high frequency repeating stations? At a first approximation assuming 100m (330') tall towers you get ~36km to the horizon, so you'd need ~150 towers with repeaters on them to cover the ~5500km from London to New York. I guess that's not _impossible_, but even if you could stack up the infrastructure required, the latency in those ~150 repeaters would need to be very small to beat the guy sending his data through the fibre on the sea floor with a theoretical ~20ms ping time, and a quickly googled practical pingtime of ~100ms. The radio options still requires the ~20ms speed-of-light propagation time, but needs to get the signal through ~150 repeaters as well, compared to just the one on each end of the fibers (I _think_ the optical repeater/amps used on oceanic fibers are zero latency...)
AWACS – or analogous commercial aircraft regularly in convenient positions?
Or far fewer towers/tethered-transmission-balloons at much higher altitudes?
Or even unmanned constantly-flying communications platforms – 'SkyStation' was one such blimp-based concept from the 90s.
Wikipedia suggests the actual service distance from an elevated antenna is a bit larger than the simple geometric estimate. Also, I think you've doubled the necessary number of 100m-high relays: if each tower reaches the horizon at N kilometers, they reach another equivalently-elevated tower at 2N kilometers.
Seriously, though, if there was something to this, they could eventually splice some optimally-positioned platforms into transatlantic cables (existing or new). Of course then the 'optimal position' would then be more a function of available cabling than of natural geometry/geography.