The analog tape itself, has no bearing on this problem since it's out of the equation, once you've converted the content to digital.
The symptom you describe usually points to a reading problem that older standalone DVD players had, which weren't very compatible with DVD-R/DVD+R media. What's confusing is you said you've used different burners, and got the same result, but you didn't say if the affected burned disk would play back on the originating burner. For example, did the DVD you burned with the Sony, play fine in the Sony, but then hang up on every other player?
Also, does the error occur exactly the same way on each player. If it does, then you must have corrupt DVD data files. What I think you should do is render the DVD to hard disk, instead of burning directly to the DVD Platter. DVD Architect will burn a DVD, even when the encoded file isn't strictly NTSC DVD compliant. However, it should warn you of that fact.
If what you're saying is that you've used the same DVD file created with DVD Architect, installed different burners, and gotten the same results. What you shoud do is try to run the DVD from hard disk. DVD Architect should create DVD folders on your hard disk of the project. You can test it simply by accessing the folder and double-clicking on the largest file you see there. If it hangs up,as you described, then there's a problem with the transcoding.
When you made the MPEG-2 file for DVDA, what encoding option(s) did you choose? Another hint that you might have problems is if DVDA insists on re-encoding the file during the render.
To avoid making coasters with DVDs, I never use DVDA to burn disks directly. I render to hard disk, test the DVD, then I use dedicated burner software (e.g. Nero, NTI, CD Creator) to actually burn the DVD once I've tested it on the hard drive.