Power scraper will run out $1000-1500+ and require a
lot of practice to do a good job. Also taking that much off by scraping would be insane. Does the lathe have a warranty? If you want a hand scraper, a Sandvik scraper runs about $85 on MSC with (1) carbide scraper blade. As a reference from a newbie, my first scraping job was leveling a 4" mill vise with 0.005" out of flatness. Took me probably 40 hours of work - for 5 thou!
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Honestly if the shop will do a decent job (especially if they'd grind it after milling), $150 is a steal. If the tailstock is split to allow lateral adjustment, it would be a lot easier to take material off of there. I wouldn't touch the V ways on the tailstock bottom unless there was no other way.
But #1, I'd be after the manufacturer to replace a defective component