Yep. That tire is toast. 

The cotton ball thing is news to me.

Here's another trick. I bought a bunch of patch kits (one for each bike) last summer. They each came with a small piece of white chalk for marking the tire. Genius. 

I am also meticulous about mounting the valve at the label on the tire. I inspect the tire for the puncture. If the valve is at 6 o'clock and the puncture is at 2, I know where to search for the hole in the casing and the intruding villain. The worst are those truck tire filaments. They took out a Marathon on my Tour Easy when I rode to Indiana in 2005.

Yep. That tire is toast. 

The cotton ball thing is news to me.

Here's another trick. I bought a bunch of patch kits (one for each bike) last summer. They each came with a small piece of white chalk for marking the tire. Genius. 

I am also meticulous about mounting the valve at the label on the tire. I inspect the tire for the puncture. If the valve is at 6 o'clock and the puncture is at 2, I know where to search for the hole in the casing and the intruding villain. The worst are those truck tire filaments. They took out a Marathon on my Tour Easy when I rode to Indiana in 2005.

Yep. That tire is toast. 

The cotton ball thing is news to me.

Here's another trick. I bought a bunch of patch kits (one for each bike) last summer. They each came with a small piece of white chalk for marking the tire. Genius. 

I am also meticulous about mounting the valve at the label on the tire. I inspect the tire for the puncture. If the valve is at 6 o'clock and the puncture is at 2, I know where to search for the hole in the casing and the intruding villain. The worst are those truck tire filaments. They took out a Marathon on my Tour Easy when I rode to Indiana in 2005.

So, it took some doing but I finally wrestled the new Schwalbe Marathon Plus onto my AlexRims DT18 front rim this afternoon.  It was an epic battle, even though I was employing the secret technique shown in the video link you provided.  I was wondering whether a soap solution wiped around the rim might have further eased the process- have you (or anyone else reading this) ever tried that?  Has it helped?

In fact I mounted it twice- don't ask me why, I won't confess- and the unmounting was probably harder than the mounting or re-mounting.  What a PITA.  But it's on, and I have no concerns that the tire will blow off the rim due to overpressuring.

AND, the wheel went back on the bike without any of the front brake drama I've come to expect when I have the 1.5" Marathon mounted.  (I had a fresh new never-been-used 1.35" already on hand; I'm hoarding the 1.5s for the just-before-the-tour swap-out.  If I end up electing to carry a spare it'll be the 1.35 I just put on.)

One further bit of progress: a few minutes with my Dremel tool has finally (it's only been 15 years) resulted in removal of the "lawyer tabs" on the front drop-outs.  I've always hated having to unscrew the quick release extra-far just to take the front wheel off; now I don't have to.  I have a rattle can of blue spray paint that is very close in color to the color of the bike so nobody will ever know.

Àn informative thread. 

I used ro ride on Schwalbe Mondials. I still have one for backup hanging on the garage wall that went all the way across the OZ outback. Great tire, but a harsh ride. Expensive here in OZ, too.

I switched to Maxxis Icons a few years ago and run them tubeless. They last almost as long, cost half the price, and deliver a supple ride... and no flats. 

Replying to myself to update this thread.  I really thought I was going to get 8,000 miles on the 35mm Vittoria Randonneur tires, but the rear tire blew out yesterday shortly after I commenced my ride.  Fortunately I was only a block from home so I just pushed it back to my garage and replaced it with a used 38mm Panaracer Tourgard tire.  The blowout occurred on the sidewall right at the wire bead that secures the tire onto the rim; 

This tire had previously had a flat from a shard of glass, but otherwise had given me very good service.  I'll ride the front tire for another 100 miles just so I can say that I reached 8,000 miles with it, then I'll replace it with a used Panaracer Tourgard as well.   

So FWIW, for my style of riding which has consisted of commuting to work with a light load (1 pannier and handlebar bag), fully loaded touring, and training rides preparing for a tour, I seem to get around 6,500 to 8,000 miles on a set of tires (35 - 38 mm touring tires).  And I do rotate tires every 2,500 - 3,000 miles.  

So now you know.  I'm not as lightweight as I should be (okay, around 225 lbs most of the time though I do drop some weight on tours), so I would think that lighter riders and bike combinations could get as much as 10,000 miles from a set of quality tires.   Maybe.