It is perfectly possible to send signals at 500 MHz or much higher through a via. However, you have to be careful.
The via inductance is almost a red herring. You are basically correct that the via itself has not much more inductance than a trace of equivalent length. The real problem with vias is that generally the return current also has to change layers. If you have a single-ended signal on a 4-layer board and go from top to bottom, the return current has to move from the upper plane to the lower plane. If both of those planes are ground, simply add some ground vias as close as possible to the signal via. If one of them is a power plane you will need to add a bypass capacitor or few near the via. Even so, the return current will have to divert quite a bit to go through the via or bypass capacitor and add more inductance than the signal via itself.
Solder plugging a via doesn't make a difference as skin effect confines the current to only the outer surface of the via.
With differential signals the return current is flowing through the other signal conductor rather than the ground plane. This makes things somewhat clearer-- just keep the positive and negative signal vias close together. Becuase you can't place the vias as close together as you run normal traces, you may have a slight impedance mismatch but it shouldn't be too bad. You can deliberately add a bit of capacitance to smooth it out if you need to.