i agree with the others about avoiding spray glue. no one knows about long term damage and some don't wash out and some do. the red may bleed, but the embroidery may also (probably) shrink, causing all kinds of puckers. looking at the picture, the embroidery is laying nice and flat, with little room for shrinkage.
i think ninnie is right about the handquilting, too. machine quilting would look wrong, imo, on a quilt obviously this old. i think backing with muslin is a good idea for added strength, and a rather flat batting with a muslin back would be in keeping. i
n your bathtub, run cold water. i would use retayne instead of a simple color catcher. but a color catcher is better than nothing. add the gentlest soap made for quilts. i like orvis. when the water and the products are thoroughly mixed, lower the quilt, finished, and gently swish it around. gently, gently. the quilt should be folded only enough times to fit in the tub, accordian stye. let it soak for , oh, an hour. swish, swish. let the water out. when the water is gone, gently step on the quilt to squeeze out as much water as you can. do it again. repeat until the water runs clear, or almost clear. years of dirt are in there. when you're done (this is the hard part) roll the quilt to one side of the tub and start moving a sheet into the tub from the other side edge. when you get the sheet edge into the center, roll the quilt into the sheet and move the sheet over until the quilt is centered, like the way a nurse makes a bed around a patient. when the quilt is in the center of the sheet, wrap the sheet so it covers the top. step on it one more time. plenty more water will come out. holding on the sheet ends (you've used a larger sheet than the quilt) lift the quilt out of the tub and onto the flat surface you prepared to dry it.
dry it on the floor with a shower curtain under it, or any other waterproofing if it's inside. in that case, lay a bunch of towels over the plastic, to keep the quilt off as much plastic as possible. if you have a carpeted room and you don't mind it getting very wet, that'll do it, over a clean sheet. not ideal for you, but inside is inside. use a fan inside. if you're lucky and can do this outdoors, lay it on a large sheet on the grass and cover with another sheet. we like birds and all, but ..... . leave there as long as possible. inside or outside, turn every day. be patient. this will take some days. keep it out of the sun. it puckers appear, gently pat them out the best you can. don't tug. that's the best you can do for old fabric whose strength is uncertain. i sounds worse than it is, but it is some work. good luck with it. do you get to keep it?
edited: do not hang it in any way over racks or lines or anything. the weight will kill it. dry it flat. if the weather looks bad and you can't dry it indoors, then wait.