Booktrunk, I looked at the Lime one you linked to myself, but discounted it because it is compression style, which is only really good for A-B cups. Anything larger and you need something with cups.
I used to wear compression tops, until I saw video of myself at the end of a race. It didn't feel like there was so much swinging, but the evidence said otherwise. Not pretty!
If you have just had an operation, as your post above suggests, then I guess you need to be extra careful about causing ligament damage, and the double approach might work well, especially at first.
I don't know if you live near a Sweatshop, but they do a free bra fitting and advice service. I haven't tried it but it might be useful, especially if you are not completely sure what size you are now. Lots of people wear the wrong size you know. I was wearing a 38B until I got fitted for wedding underwear and she said I was actually a 36D. And sports bras can measure up slightly differently to normal ones too.
Hope you find the one that suits you and enjoy your investment.