If it's hurting you, then you need to make changes. Your neck doesn't have a ton of muscle, and it's pretty easy to strain or injure it if you aren't careful. Sure, you can carry a lot of weight on your head, but it has to be balanced correctly.
I think putting a shoulder support in there would work just fine. At 7 lb it shouldn't be heavy enough to need a back support as well.
Yeah I'd definitely give the shoulder brace a go. You should always worry about issues with your neck, you could be pinching nerves or damaging the discs and muscles, and that's definitely not worth it.
In the meantime on your days off work, I would wrap a warm cloth around your neck to soothe muscles, try and boost any recovery that may be going on. If you have someone living with you, try and get them to give you GENTLE massages.
Makes me wonder who the hell designed it to have all the weight supported by the head, really. :/ That is so bad.