Fixing a torn DAT tape

So, it happened after all, no April Fool's (wish it were, it's my favourite recording). It happened on rewind just before it was done.
Any idea how to tape a torn DAT or if it's actually still possible at all and what chances there are any recording is still intact? It's right after the leader-tape although on the magnetic tape itself already (3-5mm in directly after the leader-tape).
Bums me out to be honest.

I did read on the net that you should only tape it below the tape to avoid damages to the rotary head and irregularities, but some questions remain:
Which tape is recommended?
What chances are there for an amateur to fix it (or is the required skill level too high)?
If the StartID track marker was affected, any idea if it is still fixable? Theoretically that would imply the device would read it as "empty".
And finally, should a part of the tape be discarded or not? I've read conflicting information on that.

EDIT: Ah snap, I accidentally posted it in the wrong section, this was supposed to be in "Other formats". Guess I was a bit out of it due to the sudden situation. My bad!

 

Thanks @Mister X , that's a good pointer for this salvation project and thanks for this fast reply!

I've further inspected my (un)fortunate case. In fact, there's very little to almost no crumbling at the torn spot, which leaves me optimistic. I measured the (continuous) black segment starting from leader to torn part. It makes for almost exactly 7mm (after all, more than expected, but still below 1cm).
Just in case it's of use for others with similar problems: From another resource I've gathered this equals actually a little less than 1 second of recording (8.15 mm/sec tape speed) assuming an equal output ratio of movement speed to music, eventually ~1.6/1.7 seconds as if I recall correctly it was an LP record. If out of luck, this is exactly the part that contains the StartID leaving the tape "blank" for devices. If lucky and it does actually contain audio already, it the devices error correction could help.
However, the cut is actually surprisingly clean, there's only one tiny irregularity/step on its border facing the plate that gets pulled back on insertion, which might make it easier to put it back together at this spot. More so if I find out how much space itself is being used for actual track recording and how much is just "convenience/backup", this might not matter and could be cropped for security reasons.

So I guess I can set up a to-do of this kind with this information:

• Aquire tape splicer.
• Figure out ideal tape to put on the backside to reattach both ends. I rather not use Tesa for this, doesn't sound like a solid solution at all.
• Figure out (if possible) exact StartID placement in physical space/distance from leader tape on black tape.
  
• Figure out exact helical track placements/dimensions in physical space (I doubt they go border to border after all, that would sound way too risky for practical use and could result in loss of data).
• Find a best practice to digitize the entire tape in lossless format straight in one session for later transfer onto another, preferrably fresh, still sealed DAT (found a resource for fantastic offers that same day before that happened).
• Looking further into chances of head drum damages from bad work, which is why I would only want this to be digitized once.

However, I'm tempted to wait until the international crisis calms down a bit before I actually purchase tools for this, just for safety reasons (and because delivery services are pretty stressed during these times, it just sounds like a bad idea to do hobby-purchases that can wait a bit longer). I guess the corona outbreak will allow me enough time to experiment with directly recording the audio output with my computer too, so I'll focus on that for now.

If anyone has any other (obvious) pointers I may have missed, they're dearly welcome information! Time to get back to some extended research for the next hour.

 

My DAT doesn't record directly from the beginning of the tape.
Maybe yours too. Open it, load a fresh tape and look if and how much of the tape it spools from the beginning before it's ready to record.
Maybe you could splice the tape directly to the leader without loosing any recording ... ?
My DAT is able to record without StartID and play back such recording without a problem.
For splicing I use good quality "Scotch tape", I've never spliced a DAT tape but a lot of cassette tapes.