First of all, congratulations on starting up running.
Everybody is different, so it's hard to be precise without a lot of info, such as age, weight, athletic background, medical history, etc.
I need a bit of clarification before I can give much advice. When you say 'max calculated' heart rate, do you mean the typical '80% of max' which is recommended for cardio benefits? If 184 truly is your 'max', then I'd be concerned with going into the 200+ range.
How long are the walk & run intervals? If you're getting into the 200+ range in the 4th interval even after 3 walking breaks, I'd say you are pushing it too hard.
Do you have a specific time you're aiming for in the half?
I can base some things on personal experience. After avoiding all things cardio for 20 years, I started running 4 years ago. I have run 3 half marathons in the past 3 years & my heart rate doesn't get much above 160-165, which is pretty well 85% of max heart rate for my age. However, I run it right around the 2 hour mark & train as such. If I wanted to improve significantly, I'd have to raise the intensity & thus the heart rate. I still wouldn't go much past the mid 180's though.
Anyway, there's lots of active & athletic people on this site. I'm sure others will chime in with their good advice.
Good luck with the running.