I need pictures.
The matts should be "toed" in 6" deep at the edge of the driveway. Look at the detail and instructions for installation (number 2 on the attached link) That trenched edge should be right up against the driveway pavement.

Generally the tubes are used to protect plants from wave/scour action along a shoreline OR used to terrace a slope.

Here is a link that might be useful: installing an erosion control blanket properly

I don't have pictures, sorry! There are areas with no-to-little slope. The steepest sloped sections are approx. 9:1.

That certainly looks to a quite thorough approach! Unfortunately, even more certain is it not being able to be done that way. :-(

Are you - or someone else - willing to make a "next-best" recommendation?

I have alot of personal experience with dealing with soil erosion. What is causing the erosion?
My issues were with slopes that had lost all grass, top soil, and vegetation, and when it rained my yard was covered in little rivers. I can see the sandy layer floating to the street. I built dams out of rock, logs, stumps, 4x4's, and mulch. This helped control the continuning erosion so I could build up the soil with compost, top soil, soil conditionier, plants, and mulch. I am also building a non-traditional rain garden to take care of the roof run-off. Along the driveway in the worse spots I put rock and gravel, and redirected the water run off from the drive way to the rain garden. It was not a quick fix, as I have been at it for 2 seasons now and I am half way done.

Pictures, please?

How big and steep is the slope?

What is the degree of slope that you need to protect? A gentle slope (1 in 10) is much easier to control than a steep (1 in 4) slope would be. One a gentle slope those erosion control mattes will work very well, and maybe are not even needed. On a steep slope something more is needed since those mattes will simply allow the water to flow through and if heavy enough that can erode the soil so tubes may well be needed. You may well need a combination of the two if the slope is steep and long enough.

Again, I don't have pictures--must be a lot of concrete, visual thinkers here--sorry to disappoint.

The steepest sloped sections are approx. 9:1, as already mentioned. This section is about 40 feet long.

Something is definitely needed. Soil and mulch washes out along the edge of the driveway, esp at this edge.

I'm concerned the mats will allow soil to continue to wash away as I don't have the resources to install it in the recommended manner as per joepyeweed's link.

I've started looking but have not yet found a local, affordable source for the tubes. I'm not going to order these online and I need them to be a smaller diameter than those I've seen along public roads. We'll see.

Don't let the search for the perfect get in the way of stopping the erosion:

It's only 40 feet long. Get a bunch of straw bales, lay out thick "flakes" of straw on the slope. Cover them with bird netting and stake it down tight. You can use small branches for the stakes. Slice the netting and plant your ground cover through the straw.

Also look into "gabions", twig dams, ... anything to stop or slow down the water as it comes down the slope and onto the driveway.

lazygardens, you probably intended your post to be helpful...

Have you talked with the people at your local office of the Soil Conservation Service or Natural Resources Conservation Service?

Why not invite a landscaper in for an estimate. Have them explain their plan. Estimates are free and you can still use the ideas. More than one estimate may give you differing approaches.

Alternatively, place a wall (stone, wood, concrete) and raise the height. Remove the slope and limit the erosion. A nice drive edge bed is then ready for your plantings, floral or grass.