I've seen it done both ways. To me dropping it out the bottom is the cleanest. Basically disconnect all wires and plumbing, unbolt the K-member and upper spring/shock mounts, and use your engine hoist or an overhead hoist to raise the nose of the chassis high enough. Roll the K-member, full front suspension engine and even with the trans attached (dolly under the tailshaft) over to an open space. Depends in part on what you are doing with the engine. If you’re doing a full rebuild, either way works.
I've seen photos of people raising the front end with jacks, and cribbing the front chassis support points as the nose of the chassis was raised. You should be able to find articles online or videos on YouTube showing how to do it both ways.
When I had a major performance rebuild done by a shop, we decided to pull from the top. I wanted them to take my car to a local storage facility so it wouldn’t be sitting outside in their lot for (what turned out to be) 8 months. Needed to keep the K-member, suspension and wheels in place to tow it.
What did you need to pull the engine for?
What turned out to be keeping you from getting the engine out, and ending up bending the cowl sheet metal?
And now you are unable to line up the motor mounts with the K-member? Or you can’t get the tranny input shaft lined up with the torque converter?