Whoa! 10-60-10? Promoting bloom and fruit is all good, but that's a wee bit unbalanced!
It may be a bit late for this batch, but you could try giving them a dose of seaweed extract (diluted as per instructions for root drench and foliar spray). Some of those micronutrients may help them out.
With potted veggies I have found the key is making the right media. Regular potting soil is not usually your best bet. Try one part sharp sand, one part garden soil, one part compost. Depending on your soil type/climate you can then add the appropriate amounts of vermiculite/perlite to get the right texture. I always did potted veggies organically and would also add amendments such as rock phosphate, greensand, blood/bone/feather/cottonseed meal, etc to the mix. With that stuff in there all they needed was occasional sprays of fish emulsion and seaweed extract to keep em happy and productive.
Another thing to be aware of is your watering schedule. Potted tomatoes like to dry out a little bit before getting wet again. If they're super moist all the time that might be another part of the problem.
I am by no means an expert but have had some good harvests in the past so I hope some of that helps. Good luck!
Edit: Whoops! Just realized that I read your post wrong. I saw the root rot in the subject line and didn't see the fruit rot in the text. So it does sound like blossom end rot is your problem. Forget everything I said and give your plants a light dose of agricultural lime as a side dressing. BER can also occur if you underwater, as opposed to overwatering like I first suggested. I gotta learn to read more carefully...