http://knitty.com/ISSUEspring05/PATTasana.html
I found a great tank top pattern to knit but was majorly bummed to see that the back exposes quite a bit of skin.
any tips on how to make the back completed closed, yet still be knitting in the round? (or change to be on straight needles?)
Surely the easiest thing to do would be to carry on knitting in the round up to the top, ignoring the instructions for the bands across the back and adding extra stitches to accommodate chest size?
Or is that too simple? 
I have no idea. I am just a beginner knitter and wanted to make a relatively simple tank top… This one looks dang cute but you have to pay for it 
How about designing a simple tank top of your own?
If you have the essential measurements, (hips, waist, bust) and do a swatch of the yarn you wish to use you could come up with your own pattern.
I was looking for, (could’ve sworn I had the link) a KAL here on knittinghelp which was for all those who wanted to design their own tank tops - I was going to point you in that direction for an idea of what’s involved. Maybe you want to try looking for it yourself?
Failing that, there’s a ton of sites out there with free patterns of all sorts, shapes and sizes from which you could take your pick.
Google is your friend! 