CTR on Display is always lower, don't worry about it. Focus either on the amount of impressions received or the conversions. If you haven't already, you should install conversion tracking on the the thank you page of your contact form.
I would look first at the groups getting the most impressions, regardless of CTR. Do what you have to do to improve things such as tighter keywords, negatives, better ads. Go on to the next group. Only problem I have with your way is that you may be optimizing a group that gets few searches. You'll eventually get to all of course but start with the groups that will have more of an immediate impact overall and those are the ones that get lots of searches.
It's a pain to work on a campaign with no conversion tracking. I always feel like I have one arm tied behind my back. Ask for conversion data. Surely they have that. Just a weekly report of how many sales were made. Better than nothing and could help identify the better performers, or at least give a better idea.
I'd go as far as to say it's "2 hands behind your back with a blind fold on" if there isn't conversion tracking. I don't really see how anyone can solely optimize off of CTR. It's a hollow metric in and of itself when there isn't further context into the conversion numbers.