It's really fairly easy to respoke a wheel. Go for it. Single cross lacing is quite simple and easy.
Your real problem though, is not only are you wanting to save the effort of respoking the whole wheel, you can't be bothered to tune it. So the same shits going to keep happening if you keep riding around on a wheel with loose spokes. The riding you just did may have damaged all your remaining spokes, so you really need to chuck em all. Or, they were just that bad in the first place, and again, you need to dump em.