Bruce, do it. Put it under the hood. Getting under there requires a lot of planning, all tools and supplies at hand and plenty of light.
I had some patio furniture pads laid out on the floor and the seats out. Then it isn't too bad. I have a pic on my cell phone of my girlfriend under there when I had a cast on my ankle though........
But on the other hand, once it's all done right and proven you don't have much call to access it.