Caphilldc,
I tried tilling two years back for no good reason. It was not right decision because I spoiled the soil density and ended up with bumpy lawn. Last year finally I hired someone with powerrake to grade it again. But if compaction is your problem,(suggested by Bestlawn here)you can try "Nitron A-35"

Kill what is growing there now. Leave the dead material in place. Do not till.

Overseed with the mix that you want.

Forget the seed. We are talking about a tiny strip. You will probably be ably to buy new sod for under 20 bucks. By the time you pay for seed and the extra water needed to get that seed going, the sod will probably be cheaper, faster and look better.

Also, normally I wouldn't suggest tilling, but this is a tiny, high stress area. You may as skim the top layer of mess you have now completely away and till in an inch or so of compost. Spend a bit of time leveling everything well and then lay the sod. Also, you will get the benefit of improved soil. I imagine that this isn't going to be any easy place to water except by hand, so having a good soil base will be extra important.

Couple of things...
If you want to till the soil, then you're going to lose your current grass anyway. Only thing is it will be mixed in with the soil which I don't think I would want. Fine fescue in the midatlantic or southern states is not very common as a lawn. Just now is there a movement to trial it in sunny areas where it was believed to grow only in shade. It's a nice looking grass though but it's probably not what you're thinking when you think of fescue. When you want to plant something in an area it is not known to be wildly succcessful, you would probably want to plant a variety that has been noted to excel in conditions that best describe your climate. I noticed that blend is exclusive to the company. Differnet varieties may do better in your area but also, if you need to overseed, you will have to rely soley on that company for the seed.
The "fescue" you're thinking of is turf type tall fescue, available from any hardware store in top rated varieties.

The reason for the eco-lawn is to have something that doesn't need to be watered to stay green. The slow growing is an added benefit. I also have a large maple tree shading part of the yard.

Sod would be great, but this particular blend has too deep roots to be sold as sod. I'm open to alternatives, though, especially if it's available locally as sod.

Here's been my experience with fine fescue. (creeping red only)
Mine that is in full sun held its color. It has held up to the drought better than any other grass. It has needed some fertilizer. More than I was hoping to give it. It took a really really really long time to establish and also germinate. It looks very plush like a meadow in scotland or something. The color is great ('Florentine'). It looks unique. It holds up to some regular traffic such as right in front of a gate that I use daily. But for high traffic it wouldn't be my first choice. I have most of mine growing in a partly shady area with a drainage problem so the ground stays moist. Knock on wood, no fungus yet there. It is actively growing! And very fast at that. It is not a "No-Mow" grass if you want to keep it lawn-short. Mine grows faster than all my other grasses, KBG, tall fescue, bent and bermuda.

So I encourage you to try it if you want but those varieties on that site might be fine tuned for canada. It doesn't mention anything other than being a proprietary blend.
I also get a little nutzso when someone calls a bag of grass "eco-something". There's nothing ecological about having a lawn. Let's just clear that up right now.
Luckily you can check the ntep ratings for fine fescue in VA.
Linke below

Moral of the story.... sod is a heck of a lot easier if you can get it easily in your area. Here in GA it is next to impossible to get sod unless it's winter time. Not including that tropical weed stuff that some people plant.

Here is a link that might be useful: VA ntep ratings fine fescue

Just FYI - the website you are using as a definitive authority is stretching the truth considerably to sell their products. They start with a few grains of truth and then pile it on.

First - this is just a fine and creeping fescue mix. Nothing wrong with that, but it is unlikely to be any more drought tolerant than any other fine fescue mix. If it is in a shady area, it might stay green without watering - but I wouldn't bet on it. I have some fine fescues under mature trees and it is holding up fairly well, but I've had to water it a few times this year already to keep it looking nice.

Second - Fine fescues need less fertilizer than KBG, but you still need to fertilize.

Third - Stores don't sell this blend because they won't pay a premium for a generic blend off the internet with no brnad name attached. They do sell fine fescue blends - usually labeled as "shade tolerant." It certainly has nothing to do with this grass being so disease and neglect tolerant that it would drive them out of business if their customers bought it - as claimed by the website.

Finally - The website claim that the roots are too deep to be sold as sod is an outright lie on their part. If you google "fine fescue sod" you will find lots of people selling it. Fescue does tend to have very deep roots once established, but that doesn't mean you can't made sod.

To touch on Bill's point #3... "It certainly has nothing to do with this grass being so disease and neglect tolerant that it would drive them out of business if their customers bought it"

Doesn't every bag of grass seed in the store have the same promises printed on the bag?

Funny they should mention that actually....
Pay particular attention to the "Planting method"