I’m sure this isn’t the right answer, but my husband has always used regular dish soap and water on our pewter, glass-bottomed beer mugs from England. Cleaned them up nicely, though I have no idea if it actually hurts the metal.
Are you familiar with sliver cleaning cloths? They are impregnated with a sliver cleaning chemical like jewellers rouge, and not as harsh or foul smelling as the liquids. Well you can get ones for cleaning pewter. You can sit and rub while peacefully watching TV, like a domestic Aladdin!
If you can’t get them locally, I’ll happily send you one, but it will take a couple of weeks from Aus.
You could try the old “Aluminium foil and Caustic soda” trick as well.
That’s just a plastic basin full of hot water, lined with a sheet of kitchen foil with about a tablespoon of caustic soda crystals added. Dip pewter or silver in this for 10 mins, remove, rinse well with water, dry. WEAR GLOVES.