I would recommend scraping it flat rather than using abrasion. The buy-in to scraping is higher, but cheap compared to how much time you’ll spend on it with whatever technique. A 12" x 18" surface plate can be had for around $100, and that’s the most expensive piece. Michael Ward had an excellent series in Home Shop Machinist several years back on the subject. I would have thought Village Press would have turned them into a book, but not yet. Searching to see if they had, I came across this page, which is chock full of references, including the very first, an 1840 paper.
The problem with abrasion is that it’s very difficult to use this to make something actually flat. Abrasion rate is quite sensitive to contact pressure. It’s why optical flats are ground in triples, because the flat on the bottom gets more pressure on the edges and tends to concavity, which grinds the top into convexity. A surface grinder has a similar problem, that you need the work surface to be evenly supported to the base. Probably the best machine would be a horizontal lapper, but it would need to be a big one. If you still want to try abrasion, you’ll want a way of evening out contact pressure. One way would be to cast the frame in a block of plaster of paris, and then only push the block around from the sides. The block will restrain flexure in the frame and the mass of the block provides even contact pressure.
Scraping has the advantage is that it uses a measurement (spotting) that happens at zero force, so you could actually scrape a reference surface onto a spindly frame. Even you manage to abrade one side flat, the next step is get the other side flat and parallel to the first face. Another flat is easy enough, making it parallel is much more difficult.
And to reiterate, even if you had a perfectly flat subbase frame, it’s not very stiff, so as soon as you bolt a wavy heated bed onto it, it’s going to move and not be flat any longer. That doesn’t mean it wouldn’t be useful, but it’s also not a panacea.