I've not run into a problem like you describe. If you haven't found a way around this here is my suggestion. First be sure not to change the settings on the larger screws which are used to aim the headlights. There are three screws on the headlight retaining rings. those are the only ones to take out. Next,
Harbor Freight sells little picks with straight and curved ends and I think they are less than $5 for a set of 4. I've found these very helpful and I think you could use them to carefully remove the stainless headlight rims once the screws are out. I would pry through the holes for the screws that were removed. A final thought if you have not messed with the headlight aiming screws is to park the car with headlights shining on a garage door. Put a cross of painters tape on the door in the center of the light shining on the door from each headlight. After you change the bulbs, if the headlights don't center on your tape marks, use the adjusting screws to get them back where they were. Finally, if you did change the aiming, I'd just go up to a garage door, turn on the lights and adjust them to where it looks good. Hope this helps.