I don't use them since I have no need, however any of the flat panel types or a sweeter heater (which is suspended) should work fine. I'd check each one you're considering for any restrictions on use, but they'd all be safer options than a heat lamp.
As far as the coop issue, I'd axe the ramp and convert the whole unit so it can be used as a ground floor coop. This is my write up for converting a prefab coop/run combo into a larger coop, but it would partially apply here as well. Just ignore the parts that aren't relevant (like expanding roost) since this isn't being converted to increase space for a number of birds. You may also want to build a floor as well to keep her off the ground, especially if it gets cold/wet there.
To turn it from 2 small "boxes" (tiny coop above tiny run) into 1 bigger "box" you'll want to remove as much of the inside coop wall as possible, plus the floor. Take out the old roosts too.
Nests might be able to stay as is, or may need to be relocated elsewhere or replaced - depends on the structure of the coop and how things inside stack up once done.
Run a new roost(s) lengthwise or widthwise across the newly open space, depending on how much roost is needed. Ideally you’d like 12” per bird but 10” can suffice in many cases.
Board up some of the external wire walls so that the roost area is protected from winds and rain. Do NOT fully cover up all the wire, you need ventilation and natural light, so at the very least a few inches under the roofline should remain open. If your climate allows for it, you can leave entire walls open with just the mesh, or make it convertible for the season by covering up open walls for winter, and then uncovering for summer.
Example of a modified prefab: https://www.backyardchickens.com/threads/my-renovated-prefab-coop.1440258/
