Prompted by Biggsy's suggestion : -
Controversial:
With your next chain, you could try NEVER thoroughly cleaning it or saturating with more lube. The original factory grease inside should prevent squeaks for the first couple of thousand miles.
I've just fitted a new chain to the primary bike. For the first time in a couple of decades I haven't added any extra chain lub. I shall see how long it all survives. Since typical chain life for this bike is about a couple of thousand miles, there is potentially a signficant benefit if I can get away without oiling. I don't do chain cleaning anyway, but this regime might reduce the level of oil/ferrous(ferric?) stains on my clothing.
Hopefully a gentle wipe of the outside with a rag plus a bit of water-soluble degreaser won't have affected the internal lubricant, but will reduce the crud accumulation problem. I can guarantee that the sideplates will rust visibly, but that should only be superficial. A more serious concern is whether the lack of externally applied lub. will affect chainring & sprocket wear. That won't be measurable: the current sprocket is now on its 7th chain, and the chainring is far older, probably 25 000 miles.
It's a bad time of year to start. We are in the middle of the meadow mowing season, which means pushing the bike along the paths in the meadows & collecting long grass etc. in the transmission. That's mainly fixed wheel specific, but is going to make my experience pretty unrepresentative.