Barb, your experience is probably typical. It is not a simple process to convert a Wikispaces export into any other host. It's a bit like translating between two languages, neither of which is your mother tongue. If you do it yourself, you need to know the two languages and the quality of your translation will depend very much on how well you know them both and on the effort you put in to make it accurate and stylish. The same is true for any interpreter you may hire to do it for you. No two interpreters are going to produce the exact same translation and the errors they make may be different. MyWikis, EditMe and CiviHosting all offer translation (migration) services from various flavours of Wikispaces exports (which themselves have evolved somewhat recently) to a small set of other platforms. They have MediaWiki in common and one or more also offer DokuWiki and WordPress.
I cannot tell you which provider currently does a better job of importing or which platform is best suited to your needs. I had free migration trials on all three hosts (thanks to their cooperation) which I've reported on but they are over and each has been improving its import process. In all cases, substantial work would be required on my part to fix problems and develop the navigation/menu system and other things to get the site to look and work acceptably. Their improvements have been informed by the growing number of customers each has helped; given the many features of Wikispaces, there have undoubtedly been many problems.
I have also been exploring DIY on various platforms which has made me realize just how many pitfalls there are. In my case, I seem to be having the greatest success with WordPress, adapting the instructions reported in this forum by @lectrichead - but I'm still far from happy with it and it is challenging to get my head around how WordPress works and the gazillion options there are.
So I fear that you are in a pretty large cohort of Wikispaces Refugees who are discovering that there is no equal to Wikispaces and that, regardless of who carries out the migration, they have to learn a new system, a new way of doing things and will have considerable work to do on their new site to make it usable.
Looking to move SQLite Tools For RootsMagic from Wikispaces