The common term is binding posts, isn’t it? More often than not, they are designed to take spade terminals, banana plugs or even bare wires. Unscrew and tighten for spades or bare wires, or plug in the bananas (the holes are occasionally blocked with plastic plugs that you can remove).
If you are doing DIY then search for that term, you should find something suitable for your use case.
The BP1 is/was an adapter for Naim banana sockets to allow you to use spade connectors. It pushes in and covers the banana sockets.
Those BP1 adapters were designed to fit on Ovator speaker sockets and are a little different to the regular plugs which fit on other Naim speakers and amps.
Most speaker sockets take standard 4mm banana plugs. The only difference with Naim plugs is that the black plastic box holds the plugs at the correct spacing. If you were to use sockets with a different spacing, you can just remove the black box and plug in.
Have a look at WBT, they make a big range of quality binding posts. Some will include a 19mm or 30mm spacer as these seem to be the industry standard spacings.
My Naim speaker cable needs either new banana posts or a re-soldering job at the speaker end.
What cables and connectors are you using, do you remember if they are solder, screw or another type.
While not particularly tidy, there appears to be nothing fundamentally wrong with the soldering, at least from looking at the photo. The joints look to have flowed properly and are not dry. If it is the appearance that worries you, then some heat shrink tubing will tidy it up. What I don’t like though is the very thin jumper cables, some decent ones would mot likely improve the situation.