I admire the personal grit you have Lawrence ...
I followed your advice a long time ago .. as I have 'turned off' in Settings>Cellular the Stocks App and all the others that I have no use for ... and the Stock Market App still works never the less.
At least on my iOS 8.4 for the 5s iPhone it does.
'Find my iPhone' App is on as is the 'CARR' App (California Roads and Highway from Cal-Trans) and a very few others that I voluntarily use such as the ICE Blackbox App (for neighborhood watch that I volunteer in).
Oddly enough in the Setting>Cellular is an icon for the Settings App that is 526 KB in size and there is a means to turn that one OFF .. which I have done and all heck breaks lose on my iPhone ... nothing works. The Settings App ... MUST be on with Cellular to get anything done with the iPhone.
As Settings App must have Cellular data connection going on .. to work the 'Find My iPhone' stuff and other Apps that I want to use is my guess.
So ... give it try your self ... and turn off Stocks as you have suggested .. and see .. if Stock Market really stops working for you.
For me .. it do not.
Like you .. I went to school and read books ... and I am pretty sure as unlearned as I am with a complex device as a Smart Phone I am doing it right .. and doing it exactly as you have recommended.
Stock Market pull down ... it works constantly for me and right now it shows the closing NASDEQ as 5,163.18 and the NYSE as 11,024.34 ... both of them in the green at about +65 ...
DOW J is listed and AAPL which I guess is Apple Inc is a plus 1.69
SBUX and NKE and more with 'show all' is available below that on the pull down screen.
I do have it OFF .. the Stock Market App selection as in the Settings>Cellular>Stocks 8.5 KB ... It was in the green switched on when I got the iPhone with the factory settings .. and for months it has been in the gray off position.
It is OFF right now as I write the current Stock Market values of today, and has been off for months.
Since it works any way ... despite being off and it is an Apple App that can not be deleted .. so it holds that the other Apple Apps .. such as the Health App when off ...
really .. really ... are not off.
So ... see if you can turn your Stock Market pull down off ... and if you can ... let me know.
I know your Stock Market pull down is working just as mine is right now ... so make it stop since you purport it can be done.
Once .. you actually do make it stop.
Mine do not do this ... I swear this is my witness that is accurate and complete to the best of my knowledge.