You can get both out from underneath the car - while I don't know for sure, I'm pretty sure you don't need to remove the cross member under the car. You may need to twist the starter motor a bit to get it out - as you have noticed, the space is rather tight down there. The alternator should be easy to get out. I replaced the starter motor on my J117 last year: It wasn't easy and at one point I thought "this is impossible!", but it worked out fine, and the new one slid in easily.
So just get it jacked up and get down there
- Anders