Thanks for all the responses you guys.
I got more information about unions on this bulletin board than on the well driller’s forum and all the ‘do-it-yourself’ plumbing books I could browse through at Schuler’s bookstore. You guys are great!
This is what I ended up doing… I bought 3 new unions (brass seated) at Home Depot (they were made in China, sigh). I disassembled all the plumbing between the (3) wells and the pump, cleaned up all the nipples, tees, and couplings. Reinstalled all the plumbing including the new unions using a slow setting pipe dope and yes, I even put a very thin coating on the union nut’s threads (not to stop leaks but rather as a ‘lock tight’ measure so that the union nut won’t vibrate loose over time… remember there’s a pump motor running at other end). Snugged everything down using two 18″ pipe wrenches (no ‘cheater bars’ this time) and IT ALL WORKS!!!!! No vacuum leaks after shutting down for more than 24 hours!!!
So again, thanks to everyone that replied… I couldn’t have done it without all that good info you provided.