Yes new strings and pins, that could be an option to consider. I am a bit concerned though that it will affect the sound which I rather like as it is.
Yes, it affects the sound but I am sure you like the change from more thud in the bass area towards more clear (more overtones). That is almost the same as if you listen to a guitar with old or new strings. They sound different, but better. The treble strings don't change much in the sound. In general however the sustain gets better for all strings - the strings vibrate longer, mostly because there is no dust or rust on the surface.
After restringing the tuning must be repeated several times a year, but that is finished after a year or so.
Beside the larger tuning pins you should check whether there are loose pins on the other side of the strings (towards the end of the piano). Those pins could be battered deeper in the wood or replaced by next bigger ones too (that is what they did on my piano). If those pins are loose, it rattles a bit while playing (often only a subtile sound change).