I really appreciate having a physical gym to go to–part of what made it tough to get into a habit here was the lack of a gym with reasonable access to my countryside abode.

That said, no, I don't always start with that sort of warm-up. When I can do it, I greatly prefer it (or some derivation), but like you say, when you go running it's not always easy to get that sort of stuff in.

Usually on running days I make sure to at least get a Samson stretch/OH squat cycle or two in, to make sure my hips are loose–I'll usually ease into the running from there, not going to fast too soon–usually this means a few minutes of brisk jogging to get to wherever I plan to start my sprints.

Alternatively, I'd suggest looking into alternative exercises. You might not be able to do back extensions, but you can probably do RDLs or good mornings or some other back extension exercise. Likewise for dips–it's an upper-body pushing exercise; pushups are a reasonable substitute. Pullups are a bit harder to replace unless you have some weights at home to do rows with.

We can't always operate within ideals; don't be afraid to be flexible. The goal, as always, is to work hard and improve; many roads lead to the same destination.

Although I think they all exist at a park ten minutes away, and I should probably stop being so lazy and just start my workouts there, after a light jog.