I recommend that regardless of whatever solution you choose, for those pin holes where the top (tube side) layer has an active trace to a pin, please put explicit vias connecting the bottom pin hole to that trace. In other words, don’t trust the plated through pin hole to connect the top and bottom layers.
If you are inserting a tube without a socket, you often can’t reach under the tube to solder the top layer. If you have reamed the hole to fit the pin, the plated through via gets cut disconnecting the two layers severing the connection to the active top layer.
My vote for a solution would be to add explicit vias connecting the top and bottom pin hole layers, and size the holes for the naked pins. That way, if the builder desires to build the clock as compact as possible (with the tube as close to the backlight LED as possible), then the builder can build the clock without sockets. Given pin size variability, builders may have to ream the holes. Users who want some sort of socket will have to ream/drill the holes as needed, but the added vias will connect the layers if the drilling or reaming breaks the plated thru hole connection.