To be honest you are going to seriously struggle, it's possible but hard. I've had similar issue's trying to make sweet potato mash.
To begin with you are going to need to run the sliced turnips under cold running for a little while (20mins) not sure why but it does help. (also helps with potato and beetroot crisps.
Instead of going in the oven full wack from the start you'll want to start low (130c) for 20-30 to help dry off excess moisture. Then remove the tray from the oven. Turn the oven up to 200c let it get to temp. Now toss the crisps in oil, season with quite a lot of sea salt (a lot of it will fall off so don't be tight throw it on) and return the crisps to the oven. Check ever 5min turning each time until they start to colour. Initially while still warm they will still be a little soft but once they cool down they will start to crisp up.
Also worth considering is a product from msk called 'crisp film' which really gives this kind of thing that "walkers" style crunch.
Side note: I think I used the word crisp far too many times ...