I used several of these hole plugs:
However, they are not sealing very well toward the end of the line (presumeably because the pressure builds up there). Should I use the larger end of the plug? Or is there another method of making a perfect seal?
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The holes you are trying to plug are a place where you (or someone) removed an emitter or connector. Depending on the procedure they used and the temperature, the hole in the mainline may have been torn in the process.
You should remove the leaking plug and visually inspect the hole. Turning the plug around and using the bigger end may be enough. It is also possible the plug was damaged if pliers were used to handle it. If that is the case, simply use an undamaged plug.
If this does not work, you may be able to cut the mainline at the damaged hole and use a straight coupling to reconnect it.
Otherwise, you will have to remove and replace the section of the mainline with the damaged hole.