I was working on the assumption you'd started at the inside of the track end and it had stretched far enough back that the tugs were no longer helpful, from what you're saying your wheel started much further out in the track ends?

To give you an idea, some schools of thought say change your chain at 0.5% which is 0.0025 inch per link, that's more like 1/16th inch over 12 links if you want the easier route. Seems silly yes, but since chainstretch is just the rollers wearing down on your chain, they can then prematurely wear down your cog and chainring as well.