Personally, the front tire being plugged or patched scares me more than the rear tire being fixed. I am riding on a car tire on the rear and I did get it plugged a long time ago at a car shop. They told me a patch would be better but, of course, being a car shop, they could not remove the wheel and do that. So I was told it would be five bucks, cash only, no warranty, no receipt. Many miles later, everything is still fine. But in your case, I would suck it up and buy a new tire. Just my 2¢.
2010 Kawasaki Vulcan 1700 Nomad