I of course agree with the above posts. The 1/4 mile point on our airport is exactly at the eastern edge of the pavement. The 45 degree point depends on how wide your pattern is, of course, and I suppose if you are running a mile abeam on downwind the 45 degree point is a mile out.
For me, when I am number one I can get there any way I want. That is now much safer since helicopters are always pointed out, and usually on the same frequency.
When our tower says "make short approach" I point the nose at my touchdown point, add power, and hustle.
We are now close to the number one GA airport in the world, measured by operations count and complexity. I, and my students, now enjoy what is being called "the inside pattern." You can imagine - but we get between two and three landings for every Cherokee landing.
We normally do not get short approach clearances, but if we are #1 with a clearance, we are well inside AIM and Airplane Flying Handbook norms.
It is a lot of wasted words for a Cherokee to ask for a short approach when they are intending a one mile stabilized final - and even more wasted words when they are not #1. I believe the tower reps are going to address this. As yet we have not defined a "normal approach."
As for running into adjacent class Delta when on a long downwind, it happens. The tower can get you a clearance. The Cubs get carefully planned 360 holds. We have Piper Cub experts in our tower, and they trust us to "do it now."