Which is one of the reasons they ran Gemini (the rest was EVA experience, mission duration, "precision" landing and pilot control). The chosen approach of LOR also depended on rendezvous, except much farther away from home and support. The only approach that didn't require some sort of rendezvous would have been direct ascent…and that was rejected for a bunch of other reasons. So, no matter what you do, unless you are completely crazy (or using Atomic Rockets), you are stuck with rendezvousing at some point. So, you are going to have to do some kind of flight tests to figure out the issues.

>Just a handful of missions,
>only one of the astronaut corps at the time (not sure who - was it
>Grissom? or White?) with an instinctive feel for the technique, no
>more than basic assembly with the Agena docking missions.

Aldrin, in the third astronaut draft, had written "Line-of-sight guidance techniques for manned orbital rendezvous" as his Ph.D thesis in 1963. I don't think anyone at the time had an "intuitive" sense of how orbital mechanics worked (or the history of the Gemini flights would have looked quite different).

>I think
>there was exactly one attempt - it worked, btw - at actual orbital
>manoeuvering of the docked Gemini/Agena. Anything more sophisticated
>than that had to wait until Apollo.

Gemini missions with rendezvous or docking of some sort: Gemini 5, Gemini 6A & 7, Gemini 8, Gemini 9A, Gemini 10, Gemini 11, and Gemini 12. They had a lot of problems making the target Agena and its stack work consistently (and Gemini 8 had a vehicle problem), but managed two Agena docking missions (10 & 11) where everything worked and a bunch of partials. They tested automatic system and manual approaches to docking, different kinds of manoeuvering, and proper pilot controls. It was a complete success and proved out most of the manoeuvers and techniques that would be necessary for Apollo. Obviously, the actual lunar landing parts were untestable with Gemini hardware. Sadly, the Apollo contractors didn't pay a lot of attention, NASA ran the projects in a fairly stovepiped fashion.

>How long and how many more flights might it have taken before NASA
>were confident enough to try even an all-up A8 type mission? Remember
>the deadline they were working with.

An Apollo 8 type mission was proposed to be done with the Gemini/Titan IIIC stack (with some risk and a lot of discomfort, the gusmobile was small) for early 1967. The other plans for doing lunar landings with the Gemini derived hardware strike me as pushing too far, but the A8 type mission should have been straightforward, particularly if they did an unmanned one first to prove out the upgraded reentry system that would be needed.

Edit: fix some misremembered dates.

-VR
Why, yes. I am a space nerd. And for the other space nerds here, I recommend Eyes Turned Skyward for your post-Apollo alternate timeline needs.
"They copied all they could follow, but they couldn't copy my mind,
And I left 'em sweating and stealing a year and a half behind."