Operators are well trained, and a spec sheet follows each order through the production process with the details of which steps it requires, what the test settings are, what the measurements are etc.
That doesnt sound like what I would call "paperless"
...but its a sound way of working that I have used in the past and it solves a lot of documentation problems.
At this point, from all I have read, I am still entirely unclear as to what the blazes our control plan would look like if we did have one. I made up a set of "family" control plans based on the "must have one for every product" scenario, but that would be ridiculous overkill to have posted at each production step

as the operator really only needs the details for their part of the process.
Youre almost there. The CP is what comes out of your
FMEA process and lists all control activities for one product or process. While it may be appropriate for simple process or products to have CP=WI, normally the WI is an extract from the CP with additional information for operators (like drawings, photois, diagrams)
And the CP I have thus far only includes the production process. If I try to include receiving and shipping it definately will not fit on one page.
Why should it?
Again, what does your FMEA say? If your Recieving and shipping processes are so fool-proof as to not need running controls they may not need to be in the CP.
Are recieving and shipping potential sources of non-conformity?
If there are any auditors "listening" I'd like some feedback on this thought - Have one CP that details the receiving & shipping with a generic [see family CP &/or spec sheet for production details] inbetween.
I think youre missing the point here. The hierarchy is Process flow / CP / WI. The PF details stages of the process, the CP shows you where and what to test and the WI how.
Depending on what you already have in place and how complex the processes/products are that youre dealing with, the CP could be a digest of your test WIs or your WIs are annotated extracts from your CP. At worst its copy and paste.
Whether your production needs this on a product or process basis only you can tell.
Hope this helps.
Andrew