Convert from OpenOffice to Pages

It's tough to tell where the problem lies. I don't have a perfect software recommendation, since Apple's tools generally support accessibility on par with the best third party apps around.

How much research have you and your friend done on making sure your display is configured correctly in VoiceOver?

I'd start with this support article to see if the display you have chosen is even supported but do know from past experience, that you will face many many little issues like this where voiceover is skipping some little element of formatting and can't convey all of the nuance of a document that is kerned, font tweaked with ligatures, variable line spacing, etc...

Usually this is something you can adjust the documents or the VoiceOver software to accommodate better, so the next step might be to flatten the document to a plain text file and compare how Text Edit works as opposed to Pages.

You may need to reach out to Apple directly (their discussion forums like here are not official support channels) and ask if the accessibility team needs you to file radar (Apple's name for bug reports) if you find a fairly common item that is not being supported correctly by the software (Pages / Text Edit / VoiceOver in your case). By sticking to Apple software, they might have a better chance of fixing some little omissions that could help you with your choice of braille display. Some of the retail stores have knowledgable people that you could arrange a short workshop or troubleshooting session with and AppleCare is available at cost once the free support window has passed for your hardware.

Pages is free, so go get it if you can.

In addition to the iOS and macOS pages app, the iCloud version of Pages enable anyone on Linux, Windows and Mac to use a modern browser and edit/convert pages documents without needing local software.

This beta started rolling out to people that had brand new iCloud accounts in late July at https://beta.icloud.com and now Apple is slowly rolling out the beta to anyone that logs in to https://www.icloud.com

The actual web apps are the same whether you enter through the beta URL or the normal URL and the only difference between the two is the treatment of the rest of the iCloud icons. The www url has linen and iOS 6 styling and the beta URL has iOS 7 styling without needing Mavericks or iOS 7.