Try one without any foundation and you will know why it's important to use one. I use MSQC 10 inch papers because they are convenient, all the same size ready to pick up one and use. I have used thin muslin but I had to wash it, iron it, and cut it. A big time waster for me.

I have used both paper foundations to tear off and fabric foundation that does make it a bit heavier but not any difference in ability to quilt. I have used both methods side by side in the same quilt too. I prefer the fabric foundation.

I bought Ricky Tim's product and used it in an appliquéd Quail quilt, it does add quite a bit of weight and stiffness, although he mentions it will soften with washes eventually, it is polyester so does not dissolve...and it is pricey.
I have used telephone pages very successfully and never had a problem with ink transferring to my fabric or hands, I don't mind the ripping off of the paper, it is kind of calming in the evening. I have also used thin muslin and left it in the quilt, it does add weight but also adds warmth if you are looking for something warmer than just a thin batting. I cut my foundations a tad larger then once the fabric is all stitched in place I square the blocks to the correct size.

Alternative Method?
 

You didn't mention what your plan is after finishing the string blocks or if you're going to sash them or not, but as an alternative, you could simply stitch them using the stitch and flip method straight onto batting, and then you'd already have the quilting done and can simply join the blocks as QAYG style like this: https://www.stitchedincolor.com/blog...as-you-go.html

Just cut squares or rectangles of batting, line up two strips, right sides together, stitch with your regular quarter seam allowance, then flip the top strip over and either finger press or iron it down. Add your next strip, stitch, flip, press, etc. After joining the blocks either with the down and dirty method I linked above, or with a more traditional style with the sashing strips to hold them together, you could choose to either re-quilt the whole thing or simply quilt along the seams to hold the backing to the rest of the quilt. Your strip stitching will hold the batting securely to the top, so you wouldn't have to re-quilt the entire thing if you didn't want to. Up to you!

I do a lot of foundation piecing- I like the stability. I Hate removing paper. So, I generally use inexpensive muslin ( often 0.99 a yard) or even scraps for my foundation. I’ve never had a problem quilting the quilts ( by machine) string quilts are heavy with or without stabilizer - I haven’t noticed a huge difference in with or without foundation- they are heavy quilts. I love string quilts

I bought Ricky Tim's product and used it in an appliquéd Quail quilt, it does add quite a bit of weight and stiffness, although he mentions it will soften with washes eventually, it is polyester so does not dissolve...and it is pricey.

I use Rick Tims Stable Stuff when I do paper piecing. I leave it in. It does get soft and featherlight. I found an online shop having a going out of business clearance sale. I called and asked if Stable Stuff was available and the owner said yes she had a box of ten and I bought it all at her wholesale price. I always call shops going out of business for speciality items not listed on the website that are expensive to buy retail. More often then not I find what I ask for.

My DD is a Chiropractor & massage therapist. She does very, very little Chiropractic work & left me a big box of disposable face cradle paper on rolls & I use it for the string blocks. It tears out really, really easy & is very thin.

I'm probably one of the few that prefers to use nothing, but then I have many years experience sewing lingerie fabric, and bridal fabric years ago when the stuff was not near as easy as it is to work with as it is today.

This is the one I just finished for DD and SIL. I cut old tissue paper patterns into 9 1/2 inch squares and used that as my foundation. A few bonuses to this method--no cost to speak of. (When I say 'old' I mean 'ancient,never to be used again patterns'. ) They tore off extremely easily and if there was a wee piece left here or there, it is going to pretty much disintegrate in the first washing. I prefer it to the fabric method because I was not adding an extra layer.

That is a lovely quilt, GingerK. I especially like the look of the nine patches in the corners.