Hi KO and welcome.
I am sorry to hear of your husband's axiety and reusulting depression.
You are both wise to seek out help for him, so that he can start to feel better both in social situations, and with the anxiety and depression in general.
I have heard of EFT, and some members have found help through it, but I would not say to the extent of the more well known CBT.
To my understanding EFT and RRT are used more for 'unlocking' and freedom from traumatic past experiences. (PTSD related issues) If this is the case with your husband, then this would be a good choice...if not, then you may want to seek a therapy more specifically just for his SAD.
(social anxiety disorder)
Has your husband done any therapy work at all thus far?
I went through two coursed of CBT (for panic not social anxiety) and found it extemely helpful.
I have heard that group therapy based on CBT for social phobias is highly effective!
I am not trying to steer you away from either of your ideas, or sell you on mine...I am simply telling you of what I am familiar with.;)
Keep checking back and see what others have to say as well. I wish you both the best, and invite either of you to post with us anytime!