As above use a good quality microfibre or lambswool wash mitt rather than a sponge for a 2 bucket wash and some good drying towels instead of the chamois.
To go further you ideally need some contaminant removal products such as Tardis for tar removal and Iron X for bonded metal particles before claying. The claying should remove any further contaminants leaving a glassy smooth finish, but this in itself will not remove any swirls already inflicted in the paint.
I find the Bilt Hamber clay easy to use as you just need water as a lubricant.
This process should only be done initially then every 6-12 months as necessary.
Removing the swirls to get a near perfect finish will need a 2-stage machine polishing process. This can seem daunting at first to the beginner, but I have done this myself for the first time with very good results. I bought my Panther Black Metal 2nd hand and it was covered in swirls which really showed up badly in bright sunlight.
The one thing that really gave me the confidence to have a go at machine polishing were the Junkman2000 videos on youtube:
Wow, that was minging before, looks a lot better now & you can't go wrong with AG HD Wax
But....for them to have properly washed it, dried it & also apply the HD Wax in less than 2 hours is pretty good going. Please tell me they had 2 people working on it as it takes me way more than 2 hours to do that on my own.