Wow, SC, you are really convincing me on the non violent communication approach :-)
OP, I think SC broke that down really nicely.
One other idea that might help is to try to assess what your husband's motivations are, and fact-check them against what you may be assuming.
E.g., I understand that you're feeling frustrated and neglected, and that your needs for closeness aren't being met. It can be easy to leap from there to assuming that your partner doesn't care, in fact is deliberately neglecting you or trying to "make" you feel bad. But in actuality, it seems unlikely that either is true, and far more likely that he's just very distracted by his NRE, which can be pretty overwhelming. I wonder, since he (unlike you) is new to poly, whether he is less aware of how the emotional cycle will affect him, and has less capacity to modulate it.
For me, assessing my partner's abilities and motivations might make it easier to reframe the situation and not simply see his actions as coming from a lack of care.