There is certainly nothing wrong with being thrifty until, as you said, it intrudes on a person’s ability to enjoy life and be close to others. Something about not having enough money frightens this man so much that he has lost control of his need to control his finances. He needs some help to deal with his fear and to put him back in charge of making choices instead of being driven by a compulsive need to be frugal.
The most important reason to be hopeful is that your boyfriend has said he would get some help. That means that he at least intellectually understands that there is something wrong. Therapy doesn’t have to take years, especially if someone is motivated.
I suggest that the two of you look for an experienced cognitive-behavioral therapist. Ideally, you should be involved in the treatment so that you can be a support and so you can help the therapist understand what your boyfriend’s behavior looks like. Often a patient’s experience on the inside is very different from what others observe. If you love and enjoy this man, it is at least worth 3 – 6 months of trying therapy to see if the situation improves.
I wish you well.