Your best bet is probably to switch out all your cordage and attach something like a LineLock to each tie-down point. Those things will grip even really tiny cordage like Spectra (which is definitely a good choice for your lines).
There's an online store that sells them as a package (bonus, their spectra cord is very bright). Well worth the effort to switch it out on your tent.
According to that store (which I've bought from before with no issues, FWIW), 12 LineLocks + 60' of cord will be 1.65oz.
EDIT: An alternative that I've used to those LineLocks is another product made by the same company called a LineLoc3 (sold here). The nice thing about these ones is that you would attach them to your tent (the other ones are usually closer to your stakes) and then if you find your tent sagging or billowing in the wind, you can reach the tensioner from inside the tent to tighten it.
In either case, you have to choose cordage that won't slip. Both stores I've linked to here sell a specific cord diameter that is known not to slip in the locks they are selling. It seems that Line Locks work on the thinnest stuff and LineLoc3s on slightly thicker cord.