man... y'all over thinkin' it, big time...
hell, I grew up where there was zero flat land- we threw horseshoes over a hill and couldn't even see the other pin...
anyway....
point your rig downhill... hoist your engine on the boom (assuming castered boom) and brace it with another vehicle... align and allow the truck to roll under the engine slowly with yern foot firmly on yern brake... upon positioning it properly, chock the freakin' wheels with something substantial that ain't gonna kick out or spit.
this actually creates the angle you need to plant that thing with greater ease...
are you stabbing the transmission at the same time? I'd not recommend that... I'd stab it to the engine instead, after you're cradled nicely.
I never had the luxury of a proper boom... I had a 6x6 build up of 2x4's built like a gallows with a block lashed to the crossing beam, and a iron mule to crank it up with... gotta love it, huh?
I mention that gallows because the bottom can be built to the required angle, and is hella more stable than a boom, though it obviously lacks mobility..
even if you don't move the vehicle to the boom, or change direction of vehicle to slope- use another vehicle to brace against, with a nice pad in between such as a blanket and a 2x8.