Changing the recording time "capacity" does not affect playback or readability at all. It is just changing the quality at which the recorder encodes the video. Just a chance convergence of correlation without causality.
There are two likely suspects. The blank media you are using, and your RCA DVD player. Some players (older ones especially) just flat out have trouble with burnt media. The recorder itself was obviously built with burnt media in mind- which is why it does better with playback.
The blank media you use is actually somewhat independent of the branding. There are only a dozen or two factories in the world where blanks are made- sometimes multiple brands buy from the same factory. And sometimes the same brand will switch suppliers. Check out the blank media section of this forum for more info, but the consensus is that you can't go wrong with Verbatim or Taiyo Yuden media.
And as a side note, I would recommend against paper cases if you can spare the storage space. It's not causing your problem, but DVD cases are easy to come by. If you have a Blockbuster around you, just call up on a Tuesday morning and ask if you can have the empty cases when they get done processing them. Most managers are fairly accomodating. AFAIK, Blockbuster is one of the only chains still using their proprietary locking cases.