Hi Ants.
ChicoSatis' reply was exactly correct. It's not a workaround, it's "the way things are done." Looking at your steps, when you get to "select the track," reach up and put the cursor in the top area of the arrange window, where the ruler is. click and drag from where you want the bounce to start, until where you want it to end. You should end up with a green line over that area. This is how you select the area to bounce, unless you want to bounce everything, or adjust it in the bounce window, which as you mentioned, is a pain. Camillo Jr's advice about using fade ins and outs is also important, especially with vinyl, which will have maybe a high noise floor. just look in the manual at automation, if you're not familiar. David's great book explains all this in detail, of course.
You might find a program like Audacity would work well too, and you could just chop things up, quickly add fades, and save your tracks. There are also utilities like AudioSlicer for cutting up MP3s that you could check out. I find Logic's way of doing things to be fine for me, but Audacity's way may suit you better. And it's free.
Good luck with the LPs