I think it's amazing to have the bike warning flasher for tunnels like that. I saw those when I toured the Oregon coast, and on the North Cascades Hwy, and was very thankful when I saw them. It only makes it slightly less terrifying, but it's about all you can expect from a state hwy dept. You have the lights and in a dark tunnel extra wattage would probably be a marginal help. About all I can add is to take a break on the other side until your knees stop shaking. I assume you have bright or reflective clothing.
It seemed like every one I rode through was uphill and curving right.
I don't know if walking the bike on that narrow sidewalk would be safer or not. It would just mean more time in the tunnel. I don't remember ever seeing one in the tunnels I've seen. I'd try it once and see.
I don't blame your friends. My wife feels the same way about tunnels. She's nearly hyperventilating afterwards.