Do You Carry Emergency Shaft Seal Material?

Hind sight sux.
Asking these questions after the time and bux and time and bux and time and bux you have been spent.
Not much to do or deal with a catastrophic drip-less failure and still operate.
Just go real fast to a sling waiting for you.

Meanwhile, anything could work in the place of flax to get you home.

I guess the best items to stock would be some wrapping tapes as you did use before.
Maybe install a splash shield over the log also. So if it did leak, heading home would not throw water all over.
This shield may also help protect it from a stray foot or hand from leaning on the log also.

Some dripless shaft seals have, either standard or available as an option, a device that can be used to "lock" any water ingress, provided that the shaft is not rotating.

For instance, Manecraft seals come standard with a collar on the fixed rubber part, that can be manually tightened.
Though arguably this emergency lock is included as standard because the seal itself is rubbish, and it WILL fail.
In other words, I wouldn't recommend it to anyone just because it does include an emergency system.

Another similar system I'm aware of, albeit technically very different, is the optional part that can be fitted on Fluiten seals, with a pneumatic rubber ring enclosed in a steel collar. When inflated with compressed air or with a manual pump, it seals the shaft completely.
It's actually designed to allow for seal cleaning/maintenance while the boat is in the water, but it can be used also in the event of a seal failure emergency.
Though that's unheard of with Fluiten, as opposed to Manecraft.

No idea about whether any emergency device exists also for Lasdrop seals, but since you say that you are often in the middle of nowhere, it's worth at least asking them...

I understand nobody wants to jump in those waters, but foam in a can has saved many a hull.

Why not relevant? As an emergency solution, it's certainly better than any shrink wrap tape - and also much easier/faster to deploy.

Of course, I appreciate that you can only fit these devices if your particular seals are designed for them.
And I'm not suggesting to replace any good seals who are not for this reason alone.
But for anyone cruising in remote areas where lifting facilities could be hard to find, I think there's something to be said for choosing seals that allows also the installation of some kind of safe fail device.

That said, just to focus strictly on your question "what, if anything...", my own answer is nothing.
But I'm very rarely at more than one hour distance from some lifting facilities...

Well, when I said that I carry nothing to deal with a seal failure, I meant nothing specific.
I do have spare socks and undies onboard, if that counts!

One day, We got to get you to warmer climes...

Not me, if you're referring to my previous post.
But my boat is my home for 6+ months/year, and you'll understand why whenever going out for dinner, shopping, etc. I can't always wear nothing but a swimsuit...

So I have had PSS dripless on my Egg harbor and now on my Chris-Craft. I do not carry anything specific for drippless shaft seal failure but you now have my attention.