Machka's formula is simplifying things quite a bit; climbing definitely affects calorie burn, and the heavier you are the more that is true. Speed also affects calorie burn, because of aerodynamics; the faster you're going, the more calories you'll burn per mile. Having said that, her formula is a pretty decent one to use for weight-loss purposes, because it's better to underestimate the calories you're burning than to over-estimate.

You seem to be pretty focused on getting an accurate calorie count, but the reality is the only way to do so is with a power meter. Anything else is going to be just an estimate, there are just too many variables to factor in.

The number from Strava will be better than most other estimates, provided you understand it's limitations. You need to enter an accurate body weight and bike weight in your profile. You also need to understand that Strava's calculation doesn't factor in wind or drafting/pacelines. So if you're riding with a tailwind or in a group and getting a significant draft, Strava will overestimate calories.

For weight-loss purposes, your best bet is to get a power meter. Second-best, use the lower number between Strava's estimate and Machka's formula for a given ride. It's not about getting the highest calorie number possible; it's about making sure you don't eat too much relative to the work you're doing.