Lost Apps But Can't Download

I deleted a bunch of apps from my new iPad after I synced it to iTunes because I'd never use them on it and as my iPad is mostly for work, I didn't want them clogging up the memory or the screen. Big mistake.

I have now lost those apps on my laptop in iTunes. I had them on my iPhone still but then I wiped it clean to try to resolve another issue (noise cancelling mic not working) and now I don't have them anywhere.

I went into iTunes, into Apps, and the ones that are missing are greyed out with a '!' beside the name. When I right click on them and ask to open in finder, it says they can't be located. I went to one that was there and opened in finder and looked for the missing ones in among the ones that are there but they're gone.

So I did what I read here and went into Apps Store, hit the 'purchased' button and there they all are BUT they all say 'downloaded' so I can't download them because there's no button to activate a download. A lot of them were purchased, some at quite a bit of money.

Help?