When I was approved for a mortgage loan in 2012, I had taken out a personal loan from my CU only weeks before. One of my cards was close to 90%. My scores were mid 700s. I think sometimes we overthink these details when if the overall picture looks good banks will usually like your business. The lender told me, "You have so little debt and your DTI is so low that it's an easy approval." So, even though my card util was high, it was only a $2500 card. And the personal loan was just under $3k. So compared to my income those payments were inconsequential, leaving nothing to compete with potential mortgage payments. Lots of factors play into it - of course I had high scores. Paying down the cards would probably have a better effect than moving balances. But usually honest conversations with the lender solve any minor issues.
Keep in mind (regarding my above experience) - that was a VA home loan. The VA backing probably gives lenders a sense of security possibly lacking in other loans. Still - at the time I had never heard of all the things to worry about before apping for a mortgage, so I didn't bother to fine-tune my scores. It was a really stress-free process because I knew so little. 