Now, I'm wondering if I didn't think this through properly.

In your original post you said it took a few minutes to come on. I am envisioning your car parked, idling. I'm thinking "heat related" when this could be easily explained by the even more usual broken filament mode.

The two outer bulbs have two filaments each, high beam and low. The two inner lamps have only high beam filaments.

The filament in an aged-out bulb of this type can support itself from one end, so a break might be a very small gap. When you begin to drive on the road, a vibration causes momentary contact, and a tiny fragile weld occurs. This also explains why my first reaction on finding a headlight out is to whack it. I don't think I'm the only one.

Yes, try the swap.
--
Art Benstein near Baltimore

Be wary of the man who urges an action in which he himself incurs no risk -Joaquin de Setanti