Cute pic, bama!
That's a good point, about gettig a good seal for the air compressor. I have a modified air gun nozzle with a cork over it for the seal. Naturally, I had to do extensive research at fie restaurants, searching for the perfect cork.
How do I feed the string? I cheat. I use "tampons." That is, I use store-bought gizmos that consist of a foam plug and a coil of very fine string; the whole thing goes in the pipe. I just secure the loose end at the start. The complete package looks like, you guessed it, a tampon. I think they were first developed for use with CO2-powered guns.
Anyway, this fine string is then used to pull back a proper twine, or string.
I used a 'car detail kit' to cobble together a similar tip for the vacuum far end. The key here is that your 'cork' be soft enough to force into the pipe and hold. A few layers of splicing tape works well. You start up the vacuum, then go to the feed end and shoot the line.
One last detail: Make sure the glue in the pipe is dry! Completely dry! A string that gets itself glued to the inside of the pipe is no fun. You might even want to use the vacuum to draw air through the pipe for a few minutes, just to be sure. With little air flow inside the pipe, the glue can remain wet for quite some time.