Hello Asher and welcome to this forum.
Looks like you have been very unlucky with packet writing so far, so let's clarify what InCD is supposed to provide you thus what should work and what should not.
Read and write compatibility between version 3.x and 4 have to work. If you have a problem here, please detail which versions to use and what steps to follow to get the issue.
The "eject in compatability mode" checkbox disappeared, true. But DVD+RW media burned by InCD 4 shall be readable on any OS capable of UDF natively (which is pretty large number of OS).
"The disks dying during a power off or forced reboot because the table isn't written yet.": With InCD 4, table is updated at the end, when writes on files are completed, so the table does not look to contain information that are not yet here, and will never be here in case of a surprize power off. As the disc integrity will be open, meaning that something suddenly stopped the write, the media should be mounted on read-only mode next time, so you can back-up the data that are not corrupted and re-format the disc (to start again from a clean state). The disc should not "die", except if the power off or reboot occured exactly at the time the recorder laser was written the packets of the UDF structures, which is really very exceptionnal and unlucky.
To your question:
"Aren't these disks supposed to be readable in ordinary DVD-ROM drives? " That's right, they are readable in ordinary DVD-ROM drives as long as the OS have a native UDF reader (by example NT 4.0 does not have native UDF reader, but Windows 2000, XP and Server 2003 do).
"Mine won't even read in the exact same TDK drive when InCD isn't installed." This is not normal. Can you precise the conditions (OS, fw revision, other software installed, steps done after formatting the media, ...)?
"If packet writing in the InCD manner is only readable in the *same drive* running the *same version* of InCD" Of course not!
"At least I can leave a floppy in the drive during shutdown."
Well that's should definitively be the case with InCD DVD-RW as well. At least our QA test lab do that without problem. [?]