For a tablet I wouldn't convert the PDF's to another format I'd just read them as PDF's. There are some good PDF reading apps in the Amazon appstore such as RepliGo and EZ PDF, but I've found that the default built in book reader on the Fire works quite well for the PDF's I've used with it.
Converting PDF's can be a complete nightmare depending on a lot of things (PDF's aren't really meant to be converted to another format). Are they text based or image based? Sounds like they could be images (page scans?) with the problem you're describing. For text based PDF's I've found the best way to get a high quality result is to export the text to HTML (I usually use Acrobat) and then build an ePub in Sigil or Calibre's Editor where I can fix any conversion issues and get a good "master" book which can then be converted to whatever format I was such as AZW3.
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