Because the older techniques weren't close to usable after the casting, the cleanup process made for a smoother pan. Because the newer techniques were much closer to usable after the mold, less cleanup was put into them, resulting in a rougher pan.
A cheap angle grinder is good enough for the relatively soft iron alloy used in cast iron pans. Grind the surface down smooth (don't forget to wear a face mask!), then finish up with increasing grades of sandpaper until you get a nearly mirror surface on the pan. Season the pan a couple of times and you'll be left with one of the most durable, non-stick surfaces for cooking that you can possibly have.
Or you can try carbon steel which is more forgiving than cast iron. Blanc Creatives makes a great carbon steel pan/skillet.
Flea markets often have them for even cheaper. Thrift stores have them but you might pay $50--which is still cheaper than a decent angle grinder.
Do it in a well ventilated area, preferable outside. The fillings get everywhere, include into any vents of any other equipment you might have nearby. My glasses weren't enough to keep the filings out of my eyes. They are fine enough that they won't scratch or cut your eyes, but you will feel like you are having the worst bout of seasonal allergies you've ever had.
I was sneezing rusty boogers for 3 days.
You grind the bottom of the pan smooth. Isn't that obvious? I guess not, apparently. But it seems like it should be.
If i had a cast iron pan I had to flatten, I’d dog it down on my CNC router, set up a 1/4” endmill, whip up some code for 33% overlapping passes in Fusion 360, and take off .005” layers until it was flat.
Something like this: https://www.bunnings.com.au/bosch-blue-250w-random-orbital-s...
Or for a US version: https://www.milwaukeetool.com.au/power-tools/carpentry/sande...
Seems like overkill though. You could probably just hand sand it to be honest.
Tools exist to make jobs easy. There is no virtue in doing hard work for hard works sake. Plus, orbital sanders tend to inflame my carpal tunnel.