IMO, it's the perfect candidate for tying.

As a longarm quilter, of course I prefer quilting!! That said, I did a repair for a customer of a quilt made back in the 1970's with polyester squares for the top, polyester batting and cotton backing that was tied with yarn. Many of the ties had pulled through the backing. I ended up putting 19 appliques on the holes with my longarm, sewed some of the seams that had come apart in the piecing and then going over every seam with ~~~~ to keep them from coming apart in the future. I have some quilts my great grandmother made...the quilted ones are still held together with the quilting, the tied ones are falling apart. That would lead me to believe that quilting holds quilts together better...and if I am going to go to all the work to make a quilt, I would like my great-great-grands to still be able to use them.

I had the same problem with the fabric shifting, until I basted with glue. Also, I cut the batting into thirds and machine quilted on my little ol' home domestic machine, and that really cut down on the bulk I had to squeeze through the 'space' on the machine. (sorry, can't think of the word used to describe that open area)
I got the info on how to do all this from this board and I bet with a search, it'll pop up

Nothing satisfies like hand quilting. Sure, it takes longer, but oh the feeling is GREAT!

I would do what you feel like doing . Your quilt is very pretty.

I say its a great one to tie. But whatever you decide. I'd tie it.

I don't know the ultimate destination for your quilt, but I just wanted to say a word about batting. If a quilt is to go to someone who is unable to get out from under the quilt by themselves (babies, elderly, disabled, etc), you should use a batting made especially for them (Dream Angel comes to mind), cotton or wool - never polyester! If there is a fire, polyester melts and sticks to everything, including skin, causing severe burns. Also, polyester is not a natural material and does not breathe like cotton and wool - it traps in the heat (lovely if you live where it is cold) and can over-heat a baby while they are sleeping under it. Like that lovely Minkee fabric...polyester at its finest, is lousy for baby quilts!