I'm falling back on Justice Potter Stewart's definition of pornography, "I know it when I see it."
Amusing comment given this is Euonymus.
This is the type of fortunei with which I have more familiarity but I do realize there are probably 100 Euonymus cultivars out there-
I think our best bet is to take down the bush next to the door (we were considering it anyway, for various reasons, including the scale infestation). Then we could treat the hedge portion to try to eliminate the possibility of spread.
Say bflocat, I take it your entire hedgerow the same plant? If it is and if you want to try to protect the other plants, you might want to remove the most heavily infested one right now and burn it. I'd then read up on the lifecycle of this scale and try for horticultural oils timed properly on the others as a prophylactic while planting smaller (more affordable) scale resistant varieties of shrubs in and amongst your existing shrubs that can begin establishing to take over in the event you can't stop the other shrubs you have from becoming infested. A mixed species hedgerow would be best. Could help save time and $$$ in the long run if you aren't able to stop the spread.
As far as hiring a licensed pesticide applicator, Maine Designer expressed reservations about doing so and I would have to agree. Timing of whatever is used is going to be critical and it is doubtful your end result would be anything other than ongoing bills from the person treating it for the next few years. This one is tough and it does plant hop so to speak. Don't time an application properly and the lil buggers will be able to move on over to the next plant they find hospitable, if they haven't spread out already.
Really sorry this happened to you.
Editing to add something I just thought of, you trained that shrub to go up the side of your wall by your front door! Nice look to that. What about considering a plant like this for that area-
Wisteria frutescens (American Wisteria)-
Decent photo of the plant here-
Look up 'Blue Moon' or 'Aunt Dee'. Those are cold hardy.