Over the years I've done a lot of lace crocheting with bedspread weight and thinner cotton as well. The thing that's worked best for me has always been liquid starch, mixed in the strongest proportions listed on the label, or even stronger if you add less water.
Once the starch has permeated the piece I wring it or pat it to remove excess starch then lay it out and pin it into shape and let it dry naturally.
This has been sufficient to create a wonderful appearance and when the pieces need to be cleaned, the starch will wash right out and the pieces can be given a fresh starching. Liquid starch is available in most supermarkets although you might have to search for it a bit.
I have some guest towels with hand-made cotton lace on the bottoms and for those I generally just spray a bit of spray starch and iron into shape with a hot iron for a nice crisp finished look.
If you want something more permanent there is a lace stiffener that once applied (and you apply it just like liquid starch) makes a more permanent finish that doesn't wash out. I got some of that years ago at Michaels, but I still preferred the starch.
I don't think what you're proposing will work long term but please keep us posted on how it works out if you try it.
Meanwhile, happy knitting!