Design a Wordpress Mockup - Redesign of an existing site

Redesign of an existing website to a responsive design based on wordpress platform. We have a current website [login to view URL] which is made by custom code, it has served its purpose in a great way but it is getting old and needs a refresh. We see that we now have over 50 % of visitors from mobile devices, but the conversion rates are very low for mobile. We have also lost our top ranking on google for the most important keywords. We need to regain our position. The firm is an alternative medicin clinic, based in Norway. The language of the site is therefore to be in Norwegian, so we need to find a way to handle that. The website has been created by me when I was a student and had a lot of spare time. Now I'm in a full time job I don't have time to update the site to meet new requirements such customising for mobile devices etc. The current site is pulling most of the content from a mysql database. If we can utilise this information without much changes that would maybe be preferable. I'm firstly looking for a great website designer, who knows how to build a responsive site to drive conversion (bookings) for the clinic. The website should be built on a recognised platform such as Wordpress. Due to high workload I rather prefer a process that is over multiple weeks, rather than a compressed and quick process that is hard to follow up. I'm very open for suggestions on how to best structure such a project. But I would expect to first focus on design. I'm open for a design that is built on an existing template, but do not want it to feel off-the-shelf in look and feel, but should include modern features such as a good search. I'd like an offer for the redesign of the website (wordpress template), not an entire conversion of the existing site.