Floppy old elastic question

Hi all,
I have a lovely old swimsuit that I enjoy wearing but of late its starting to need some TLC and repair work if I'm to keep wearing it.

The material is lovely and thick - and it has a skirted bottom - but the straps need some attention. Whenever they get wet they lose all their elasticity and the suit flops around me... not really what I'm looking for in a relaxing swim.

The previous owner has already somewhat butchered the suit - taking out all of the lining panels and I suspect bra cups - so I don't feel too badly about altering the suit. Plus, I don't believe the elastic - pretty as it is - is original either. It has the wrong feel and it isn't sewn on all that well.

My question to you all is, do you think if I sewed some clear elastic under the straps that it would help with the flop factor? It will be a bit tricky matching thread with that busy navy and white pattern but I would like to get her back in the water without having to entirely replace the elastic straps... if possible.

I'd love to hear your thoughts!
Denise
Crimson Gardenia blog