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Multisession is known to not be always working (in my personal experience it never worked) with DVD media, but it works perfectly with CD discs.
If you can recover all data with the memorex drive, my suggestion is to copy all data on hard disk and then burn again data on a write once disc.
The most reliable alternative (even if I still suggest to use write once media) is to use a RAM disc and a proper packet writing software to use it like a large “floppy” disc, but this system is very often failing because the packet writing softwares are very often failing and you are anyway at risk to loose all data
If you can afford, the best solution is an external HDD