Here's a Strava segment with half of his climbing. https://www.strava.com/segments/654945 Nobody is spinning up there unless they're putting out a steady 400 watts. Most people can get to where they can sustain 180 to 200 watts, and people who are doing that on this segment are going 6-7 mph, which is only 55-60 cadence for 39x28. Mashing, not spinning. OP has the equivalent of two of those on his ride, and I don't expect a brand new rider to sustain 200 watts even if he is young and in good shape. So I'm skeptical of this.

A steady 4.5% grade is no big deal, but the problem with thinking that "only" 250 feet in a mile is less than a 5% grade is that it usually has steep sections. Half of that rise per mile is considered "hilly" by most cyclists. It's more challenging than people are imagining here.

Most road derailleurs, Tiagara and higher, are not technically spec'd for 28 and larger cogs. Road bikes won't have a 34 tooth ring unless it has a compact double - and most have a standard double. These are things OP should make sure to check and not assume that it has, or even can have without changing other parts.