That's IMO the principal problem with typewriter restoration. But to restore the platen seems possible without exotic tools, if you have time and patience.
There's a tutorial on YouTube, and it looks almost easy when he does it… but I doubt it is that easy in real life. The seasoned collector from the YouTube channel Just My Typewriter had troubles with feed rollers in one of her videos: if she had troubles, I fear to try, but I'm not very competent.
The other option is to send the platen to a professional. But that will cost you quite a lot, I think. I heard that JJ Short was good.
Me, I generally just accept the hardness. The trick you described to use two sheets of paper seems enough.