I assume you have already made mortgage application so your LO should have a good simulator that can tell you what to pay off to best boost your scores. I assume this from your statement that your LO could do a rapid rescore. If I am wrong, please correct me.
I can tell you from personal experience that you will see a big boost if you do pay your revolving to less than 30% AND have more accounts reporting zero than non-zero (yes, even a $10 balance is a non-zero account).
I was reading a post by someone else (in the Understanding FICO scoring section a while ago) that had 8 tradelines, each reporting $1 balance. Then paid off all but 2 TL and had the same $$ total dollar amount on the two accounts as the previous month, and the difference was about ~30 points IIRC. I will see if I can find that post for you. It might take awhile 
but you get my point. It is important that you have TL's reporting zero balances and the TL's that you want to report a balance need to under 30% of the individual credit limit (and under 30% aggregate). You can get more points by paying down to less than 10% total but you don't want to erode your funds for purchasing a home. It is a delicate balance.
I think you are right about the 3-30 day lates in 2014 affecting your mortgage scores but having low utilitization is a good counter balance to those late pays.
EDIT: I didn't find the thread I was thinking about - but I found one that illustrates the point above: http://ficoforums.myfico.com/t5/Understanding-FICO-Scoring/Number-of-revolving-tradelines-reporting-...