First of all, the only reason why it doesn’t work is probably because of the media used. Ritek DVD+R DL are not considered to be the best, period. If you want the best compatibility, single and dual-layer Verbatim discs will be your best bet.
Your writer (AD-7200A) is considered to be one of the best SL/DL burners currently in existence (and also OOS/EOL). So on that bit you’ve got your bases covered.
For dual layer discs everyone on the forum will recommend ImgBurn, as it is free and feature-complete.
One of the things I noticed with what you’ve done is burning 8x on some cheapass dual-layer disc. That’s a no-no for most cases, even for a good writer as the 7200A. I would say that’s ok for Verbatim or other quality media, but otherwise it would almost result in a coaster everytime. Stick to about half of the rated speed, or a notch below the rated speed for newer media (4-6x burns for 8x DL / 8-12x burns for 16x SL) and you’ll get fantastic results. The slowest and the fastest speed settings will give you the worst results in most cases.
So yes, quality media and slower (not slowest) burn speeds will give the best results - burning software does not affect the quality of your burns, but some will help make intelligent decisions regarding DL layer breaks (such as the freeware ImgBurn) - resulting in non-stuttering layer changes on DL discs.
DVD-R DL discs have poor compatibility with optical drives since little support has been shown by drive manufacturers, although there are -R DL discs in the market. Stick with +R DL and bitset it to DVD-ROM for maximum compatibility with writers and standalones.
DVD-R discs are believed to be have generally better compatibility than DVD+R, and there is no need for bitsetting. The current crop of standalones however support almost any type of DVD media, even +R discs that aren’t bitset. If compatibility is your primary concern, DVD-R is your answer, although the quality of DVD+R discs that are bitset to DVD-ROM is similar unless if used on some old, finicky DVD players. If DL media is needed, stick with DVD+R DL (reason stated in preceding paragraph. :p).
Short answer: use quality media (Verbatim/Taiyo Yuden/insert-high-quality-media-of-your-choice) be it +R or -R and burn at neither the fastest nor the slowest speed setting on your burner on your favorite (or free :p) burning software, bitset +R discs if possible. The key part of the equation is the media used - don’t expect gold out of lead.