Curious why you did not use the supplied bolts from BFI on the engine mount.
I've done the mount job a couple times and can say as long as you keep an eye on the jack (good point on the jack lowering) and be sure you are simply supporting the weight of the engine/tranny, you should be able to simply remove the old and install the new. Both times I have done the job there was no movement from the engine/tranny when I removed the mount(s).
This is dependent on the way you lift the engine/tranny. It must be level (how you jack) and the car must be level. Trying this with a car not level is asking for problems as the engine/tranny will swing.
The original video was 10 minutes long. Going into detail about all that stuff. I couldn't edit it down to upload but yes you're spot on. Leveling is key and use a level if need be and electronic gauge. I've done 8 mount installs now. 3x on my car, 2x on another and 2 other guys.
I have noticed oem style seem to be better in the install and in function, but that's another topic (I even use the bfi ones which are not that design too).
I recommend do NOT use the front rail bolt bfi provides. It is not the correct distance, ie, does not give the proper amount of biting threads when torqued down that the oem one does. Use all the other bfi bolts though imho.
You can use a long crowbar to flex it around but again, if you're having to use a lot of prying to get right, one of the other mounts is not right. They are a triangle, they all support each other, work off each other and are meant to be aligned with each other. Good luck guys. PM for more advice.