Hi Jason,
DVD-R and DVD+R are different formats, so you would have to use DVD+R discs for the copies. ie it's not a case of ticking a box to encode to DVD+R format but rather just using a DVD+R disc. Most recent DVD writers can write to all types of discs so this is probably your easiest solution.
DVD players have advanced massively over the last few years and a budget player today will often outperform the top of the line model from five years ago. If your player is a few years old, the player was not misrepresented - just that the technology has moved on and manufacturers can cram more into the box.
The Acoustic Solutions DVD651 or the Toshiba SD330E can both play pretty much any disc you can throw at them, and are available from Richer Sounds for less than the price of a brake lever for an AP adjustable ratio Radial Master cylinder.
If you want more info, there is a comprehensive guide here
http://www.dvddemystified.com/dvdfaq.html#4.3 cheers, Chi
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