After many, many attempts, I have finally gotten Gothic Invasion. Boy did I get a lot of AE:
My strategy was to ally anyone around me, and use them to beat Crimea. I did so and got 3 provinces, making me strong enough to ally Poland. Then, using PLC as a battering ram I no CB'd East Frisia to vassalize them, followed by Friesland. Combined, one allowed me to annex the other. After that, things were easy: butter up Austria, join HRE, get France, PLC, Scotland and Denmark(which kept it's PU's the whole game) to do my dirty work, expand, expand, expand. Once I'd gotten about half the northern HRE I became so strong I could wage wars faster than AE could cool down and I started facing ever larger coalitions, but they were no match for my ridiculous alliance block.
I only got into trouble once, when Scotland's colony attacked Norway's colony, causing Scotland+France+other allies to face off against Denmark+Russia. I got called to arms so I figured I'd rather betray one ally then two and join Scotland, but Denmark and Russia tore through me and France's armies, sieging down my country entirely, while Scotland had it's army relax in the colonies. Denmark wouldn't let me peace out without annulling both my remaining alliances, which would have been suicide in the face of the coalition against me so I couldn't peace out, even though France did. Eventually Scotland and Denmark both had low enthusiasm but Scotland refused to make peace for years. Eventually I lost all my manpower and Kuban to Russia.
Note: I was also allied to Austria in the beginning, but I dropped them for the Ottomans.
I might continue for a bit to see if I can PU Denmark, which recently got my dynasty. Spreading Orthodoxy as a "third way" in the HRE was fun, and I even got to be emperor once since I don't have AOW.
At one point, I think I had 600 AE with Burgundy.