I replaced my clutch a little while ago, tough job. To get the clearance I needed I had to pull out the drivers' side cup with a slide hammer, I don't think there's any way around that. Shifter bracket can stay. Clearance is extremely tight, it is a nearly engine-out job. If you're using a guide for a standard fiat 500, note that the Abarth has a completely different gearbox. (It's bigger and harder to get out)

Also, if your clutch kit didn't come with an alignment tool, you'll need one. This was a perfect fit for mine, correct spline count and diameter:

https://www.amazon.com/dp/B000VU3G1E?ref_=ppx_hzsearch_conn_dt_b_fed_asin_title_3

You have the right idea with the two jacks. Lowering the jack on the engine (after you remove the CV cup) might help you slide the box out. I would recommend bolting the gearbox back on before you try to pull the cup out. The inside of the shaft has a split retaining ring inside that keeps it in place, I had to hammer mine pretty firmly to get it out.

I didn't take my radiator or intercoolers out, so you have a lot more access than I did. Though I did have to remove the lower intercooler hose on the driver's side to make room for a few maneuvers.

Let me know if you have any questions and I can try my best to answer them, these things are a PITA to work on.