You've answered your own question. Strings are the way to go. I believe D'addario says their exp 80/20 are darker than the uncoated 80/20. You might also want to try their polished (semi round) string which is darker still.
You could even try nickel electric guitar strings of an appropriate gauge. After all, they're your ears. They'll tell you what works.
I am not sure of the 'best'....but the easiest and cheapest seems to me to be....strings, nut , saddle, choice of plectrum device, the type of polish you use(just kidding)....thats about it... without going into shaving braces, soundboard, etc.
Strings for sure. Gauge also affects tone, but will require new setup.
D'addario make a silk and steel set which will mellow out anything, get of the heaviest you can get. Bronze strings "played in" sound warmer than PB.