Some good suggestions. I did consider a check valve to try and keep the pump primed, but I wanted something a little more foolproof- trying to reprime it with oily coolant in the system would be a pain.
There's not that much delay between switching on the pump and getting flow at the nozzle- probably only a few seconds at most. And between parts, I just shut off the ball valve, rather than the pump. The pump's a centripetal design, not a positive displacement, so it can be deadheaded with no problems.
I ran fifty pieces, running the pump the whole time and only closing the ball valve. Worked great, no bobbles or bubbles in the flow, no waiting.
When I redo the system, though, I may drop the tube size to 1/4", so there's slightly less head pressure on the pump, but really, I don't think it'll be a problem.
As for the tip, when I switch to Locline or some similar flexible hose, I'll probably have a couple of tips for different jobs, but really, a lathe is a single-point machine; as long as the coolant is flowing towards the one cutting point, that's all that counts. And on this particular job, I wanted a narrow stream to flood into the bore, to help flush the chips out.
Technically, the inserted drill has coolant-thru passages, and I really wanted to hook it up somehow, but the design of the turret would make it difficult to connect a hose of any substantial size. Those types of tools also need higher pressure than I think I can get from my little pump, so I'm not sure it would have worked well anyway.
Crud in the coolant won't be too much of a problem, as my bulkhead fitting is roughly an inch off the floor of the tub. If or when I make a proper reservoir, I'll add a baffle that separates the inlet side and outlet side, so that coolant has to flow over the top. That's a common trick for coolant tubs- the surface grinder's coolant/vacuum tank has it, as do the oil reservoirs on my valve grinders- and should keep the output fairly clean.
