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Sage W x H x D is 160 x 180 x 6 mm, but side with buttons rises to about 8.5mm.
Libra 2 W x H about 144 x 162 mm, so smaller.
I don't have any Kobo 6″ model here.
KOReader, or any any other program, will not help with most PDFs on a 6″ screen any more than the native reader.
A proper ebook dynamically uses the actual screen size (based on pixels) as the page size when you open it. The user can change the font size, or even face, line spacing, margins etc (unless the ebook designer messed up).
PDFs, Fixed Layout or other Print Replica use a page size decided by the designer or publisher. The user can never change the font size, or face, line spacing, margins etc. The PDF can be shrunk to fit, in which case the text may be unreadable on 6″, or 'actual size' in which case you only see part of the page unless your screen size/resolution is as big as the design page. Hence sometimes even 8″ or 10″ isn't big enough if the PDF is A4 page and 6 point size fancy serif text.
If you go for 6″ then only a few PDFs will be readable in any easy fashion.
The SF TV series 'Earth: Final Conflict' the edge of the screen could be pulled out to have a screen almost 3 times bigger.
Philips did a protoype phone that rolled up. Later Sony showed a prototype that could roll up.
There are a couple of OLED phones that unfold to x2 size, but they are madly expensive and have hinge issues.
So for now if you want PDFs, you get a bigger screen, or spend a day or three proofing OCR or other copy/pasted PDF and editing and making an epub.
Even if you get a bigger screen it won't do all PDFs, just many.
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