I just went through this. My six months of subsidized COBRA was due to expire at end of June 2016. Looking through my records (I have a notepad where I date each phone call, whom I spoke to, and what they said), I got a letter from HR on May 4, 2016 (in month 5 of COBRA) mentioning that COBRA would be running out end of June and I would have to indicate what I wanted to happen at that time. Like you, I intended to switch to retiree medical effective the end of subsidized COBRA - 7/1/2016. I called HR the first week of June (because of the 30-day window everybody throws around) and spoke to whoever answered the phone - didn't have to do anything except play dumb and say my subsidized COBRA was ending and I wanted to switch to retiree medical and how do I go about doing this and I got routed to a knowledgeable person. She took my personal info and said that they will send notice to the administration group re my coverage election effective 7/1/2016 and all I had to do was go on the Benefits Connection site, under Health & Welfare, and change my payment option so I could get direct debit. One of my concerns was that with the COBRA, I always paid at the end of a month for the next month's coverage, and I wanted to know how that was going to work at the end of month 6 - I didn't know who to pay, or how much, etc. (I have this thing about not having paid for the coverage ahead of time, and wondering what happens if I fall ill before I pay the premium.) She said DO NOT make a COBRA payment at end of June, and that CHV bills for retiree coverage the first business day after the 14th of the month, for the following month's coverage.
How it all worked out, is that July 15 I got hit with a double bill - one bill was (retroactive) payment for July coverage, and the second bill was the (normal) bill for August. On August 15 I expect a bill for September coverage, and things should settle down to a routine.
The bill reflects cost of current coverage selections. If you go through the Benefit Selections or whatever that is that always happens in October time frame, your costs when you switch from COBRA will reflect whatever you select. If you leave everything as it currently is, it will be like nothing happened and you will just sail smoothly into retiree medical. (Well, as smoothly as you can, with an approximately 3x increase in your insurance premiums).
During my transition to retirement, anytime I had a question or if something wasn't clear, or dates were confusing - I would just call HR. If I was expecting some paperwork, or things that people mentioned on this site hadn't happened according to schedule, I would call. They were great. Very patient. And they also took good notes - more than once, they said 'we already went over that with you on such-and-such a date' and I would just ask them to explain it one more time. MAKE SURE YOU HAVE A NOTEPAD AND DON'T LOSE IT. It can be nerve wracking to sit around and wait for some paper or packet that is supposed to automatically show up after x days - just call them, tell them you heard about some paperwork, whatever, and they will send it. Sometimes things do fall through the cracks. If nothing else, be a pest and give them something to talk about during their breaks. Let somebody else fall through the crack.
Anytime you get a paper with a time window, call them a couple of days before the start of the window, and then right after the start of the window, to make sure you have enough time to straighten things out if there is a problem. Don't procrastinate. Stay focused.