Currently using Sony DVD+R discs
Sony doesn’t have its own disc manufacturing plant, so it buys them somewhere and have the discs branded. The old Sony-branded discs were made by Daxon in Taiwan, but they went bankrupt in 2010. After 7 years, the old stock will be gone by now. Today Sony buys (some of) their discs from Ritek (with Fuji dye), also in Taiwan. What all this means is that the quality of the disc is is more dependant of the manufacturing plant than the branding. Although a plant could produce to high end specification for certain clients, most manufacturing plants produce in bulk and those discs get branded later for several different clients. Things like the dye formula, and the level of purity of the chemicals can set the quality of a recordable disc. Not all discs are created equal: some are very reliable and some are garbage.
To identify the origin of discs, they have a Media Code hardcoded in. With a disc in the drive, Toast can read that code, and lists this as Manufacturer ID (Menu > Recorder > Disc Info > Medium > Manufacturer ID). It is a bit more than manufacturer identification, as it tracks the exact type of disc with a code. Toast will link the code to a webpage with more information, and sometimes user comments, such as reliability. Often, the first letters in the media code identify the manufacturing plant: e.g. Verbatim discs may have a code that starts with “MCC”, for Mitsubishi Chemical Corporation in Japan.
You could have had back luck and bought a bad batch of discs. It happens. If not, then it might be wise to look for higher quality discs. I recommend Verbatim’s AZO dye discs (i.e. not the Life series).
Selected Write Speed is "Best" -- so I am not sure what speed it is choosing.
“Best” should be a negotiation between the burning software, disc specs, and the optical drive. However, burning as fast as possible may have a slight negative impact on reflectivity contrast in the dye, and thus the ability read it back. Someone on a different site recently recommended that optimal may be: half of the rating of the disc, if that is supported by the drive. So a disc with 16x rating could best be burned at 8x.
In the early years of DVD players, it used to be that some player liked DVD-R better than DVD+R, or vice versa. I don’t think it is an issue anymore for current set top players, though. But you tried that already.
and yes the burned disc has both AUDIO-TS (empty) and VIDEO-TS with VOB files.
Input video has:
Video: H.264/AVC, 1280 x 720, 29.97 fps
Audio: MPEG-4 Audio, Stereo, 48000Hz
If the software made a proper DVD-Video disc with VIDEO_TS and AUDIO_TS folder, then the input file was processed (converted) correctly and the source specs don’t matter much. Except maybe for frame rate, as that plays into the NTSC/PAL format of the disc, and could be a problem for some set top players, even if it is a valid DVD-Video. But you tried that already.
(ETA: I have both the Auto Play and Play Continuously options checked.....might either of those be my problem?)
Auto Play will skip the menu and start playing the first video. Play Continuously will play all videos, one after the other, without returning to a menu, and loop back to the first video.
With these two selected, you will never see the menu, unless you force it (e.g. if your remote has a menu button). It is perfectly valid for a DVD-Video, though, and all DVD players should respect that structure. (But if you selected “No Menus” in Toast, then the player can never find a menu, of course.)