You can get out bows & cups with a lucas mill (or saw mill) depending on the level of knowledge of the operator & how keen they are to do it. Years ago I made a router jig that ran on 2 bearers & slid along rails - worked a treat! Basically tidied up with a foot plane (angle it across on 45 deg, then at right angles to that) and finished with a scraper rather than sand paper!
If you're handy and want to have a go at it (and have time), you'll be proud once you've done it & makes a great conversation. All you need is a router & flat cutter, 2/ 3000mm bearers (straightened), 2/ straight cross bearers about 1500mm made into a jig with slot in the middle that slide up & down the long bearers...you get the drift.
Here's a machine that you can buy that does the same job.