Tire punctured. What tire to get?

So I went in today for my 5000 mile tire rotation and was told that I had a slow leak due to a hole in the front right tire. The small item is slightly recessed so removing it would be difficult. That tire is now in the rear right due to the rotation. It was raining so I can see the slow bubbling. It was inflated to maybe 39psi a few weeks ago and now service checked 26psi remaining. It was near the sidewall so I can't repair it. I'm guessing I just had real bad luck so I'll have to deal with it now. The tires are Dunlop Enasave 01 A/S 15". The Toyota Dealer had Yokohama's, Bridgstone's, and two other ones. But I'm thinking about getting them at Costco, a warehouse.

1. It's not recommended by most everybody but the dangerously frugal, but can I get away with a tire repair kit? I don't usually turn too hard anyway.

2. Assuming the answer to the above is "no", what tire should I get? Should I get 1 or 2? They still have plenty of tread on them left. Are there quieter/smoother tires as I'm not looking for performance?

 

I've done about a dozen plugs before too. Tire places don't like doing it near the sidewall. This one is near the middle/inside of the first outside tread. I used to plug them this close without thinking about the negative consequences.

I haven't noticed a leak the last time I checked air. They were all consistent. However, I've put hundreds of miles in since so it may be new.

Service checked for the warranty on the computer and said I don't have it with Toyota. I don't recall seeing a leaflet. What does that look like? I'm checking with insurance just for fun...

 

I see. Getting the same one might be better? One thing is I think I'd have to get that at the dealer. And even then they need to special order it in.

See the image for where the X marks lead. Its not very clear, but those are just bubbles. the item is sunk in. Would you think it's pluggable given it's location? I'm not sure where to measure it to. I get somewhere around 1" to where it starts curving a lot. I'd have to still figure out how to get that thing out. I'll try to find the plug kit.

 

I don't know if it's a California thing, but the Toyota service center said they won't repair it. Another instance, I've brought in my mini Cooper to tire shop for a valve stem replacement. They saw my plug near the sidewall and said it was illegal. Unfortunately they took it out and said "you can get a new tire, or we can stick it back in". ! I've also had another instance where I had a nail near the sidewall of a fairly new warranted sidewall so I brought it to Costco, where I bought it. They said they can't repair it, but replaced it instead (I paid $20).

I guess I'll just do it myself today, I won't be able to patch the inside. I have to drive my family to a wedding tonight, so I have to do it well the first time . I'll post results.

 

Plugged. Used vulcanizing cement. Pumped it to 38 psi. Drove for 5 mins. Checked as 38 psi. Waited an hour and drove for 5 mins. Checked again as 37.5 psi. Waited 2 hours and checked again as 37.5 psi. Made it to the wedding. I'll keep an eye on it.