The dyna plugs are very small in diameter compared to traditional sticky string tire plugs. Go buy a T handled kit at an auto parts store. Make sure the kit you buy has a reamer and an insertion tool. On the real kits, you ream the hole to clean it out and to get it to a size that you can insert the sticky string plug. Yes, it will require some effort. But, the hole will be clean which is very important for the plug to work. Done correctly on a clean hole, the plug vulcanizes to the tire, (look it up), and becomes a permanent repair. Note that the insertion method of the regular kit has you thread the string like a needle and it goes int double thickness making it effectively about 4-5 times the thickness of the Dynaplug string. And you twist as you pull the insertion tool out, causing a mushroom head inside the tire. Once hardened by heat and time, it's not going anywhere.
I've used the Dynaplug and had it fail three for three times. I gave it to another rider that wanted to try it and never looked back. I've used sticky string repairs for decades on car, truck and motorcycle tires and outside an occasional slow leak later due to an odd shape puncture or my poor job of reaming it, (at night, in the rain, on the shoulder of a super highway), and one hole that was just frigging big, I've run them to the tire's end of life w/o issue. big holes I have the inside patch/plug done or do that myself. Most shops won't repair moto tires any more due to fears of litigation.
If you replace the tire, bet on someone at the shop taking your tire home, fixing it as I described and riding it out.