I agree, don’t cut your 30’ lines. The flat web ones with rolled front are actually my favorites, very light weight for being so long and the rolled part slides through D’s nicely. Since your mare has a large walk, you can take advantage of your long lines and send her in a figure when her walk is getting too much to keep up with, so you don’t kill her forward and preserve her ground covering walk.
I have boy’s hands though and I don’t live in the PNW so I’m no real help there. And I do have to admit, holding the bight when I’m inside 20’ is quite a bit to hold in the hand, especially as I refuse to do loops but do a ‘tamale’ instead.
I have also made my own long lines out of climbing rope. I use climbing rope because its durable and comes in a huge range of diameters, and its made in such a way that it has life to it.
I used 1/2" for a set of 25’ lines and I think they are harder to manage than the flat web, if holding the bight in the hand. I also find them to be very heavy at that length and have a tendency to lean on my horse’s mouth. Inside 20’, they’re lovely, but 20’ and beyond I find they are heavy, and actually tend to have an irritating swing at a canter.
I don’t think 3/8" is bad at all. I have a length of 1/4" I turned into poor-man’s vienna reins, but ended up becoming my in-hand work reins. They are a little thin, but work out nicely for us doing stuff like this
Another nice thing about very thin rope lines is you can attach them to the snap of your choice with a knot. With larger diameter, I use zip ties and cover the hard bits with athletic tape.
The not-so-nice thing about thin rope lines is that they can be fussy and floppy and want to find their way around your wrist, your horse’s leg, flop over your horse’s neck, etc, and generally have a mind of their own. They can cinch themselves or knot themselves up very quickly too. Which is why I only use them for up close work where I am practically touch the horse anyhow.
Larger diameter lines stay put nicely and aren’t nearly as troublesome.
I think you’d be good with 3/8". I would suggest climbing rope if you can as it has ‘life’ and ‘feel’.
I would also suggest keeping your 30’ web lines however, and when you get more confident experimenting with them. There are many ways to work a horse on the ground and certain reins come in handy certain times. You might discover you have so much fun with your mare you might want to try gymnastics, jumping, figures, etc. The light web 30’ lines will come in very handy then, and after you’ve had some practice they won’t seem nearly as ungainly as they do now.
Also, you don’t always have to hold the bight in your hand. There is a very good clinician, Clay Maier, who has a series of DVDs and he allows the line to drag on the ground beside him. You can just see it in this photo here. He has both lines off to one side, but very often in his videos he has a line on either side of him. I thought it was nuts at first but gave it a shot and once I learned how to keep my hands in a position that kept the line out from under my feet, it was very natural and easy. I did have my horse bolt on me too and I was able to control the line safely and turn him on a circle smoothly and avoid getting all wrapped up.
I don’t let the lines drag if I’m out on the trail or around the farm though, only in an enclosed arena.
If you’re not doing so already, do consider learning to hold a whip too. A whip is handy to have, and managing lines plus a whip on the ground is a skill that is worthwhile learning.
Watch any and all DVDs you can and read as many books as you can, there is a whole world to working your horse in hand and a lot of different methods.
Nice when you have a forgiving horse to help you through 
