The Molniya orbit was invented specifically because GEO doesn't provide good coverage to extreme north latitudes. The thing that makes it a Molniya orbit is the specific combination of eccentricity and inclination that prevents precession of the orbit due to its extreme inclination (and Earth's oblateness). If you're only interested in coverage at the mid-latitudes, then you don't need to bother with all that. You can use an equatorial orbit, which is easily visible from around 30 degrees, and precession won't be a serious issue.
If you don't want to go full geosynchronous because you only need coverage during part of the day, you just need an eccentric equatorial orbit with a 12- or 24-hour period. If you have a 12-hour period, each satellite will only be in a good position for about 4 or 5 hours, so you'll need two or three on complimentary orbits to make it work. On the other hand, I believe a 24-hour orbit would have to cross through heavily populated GEO space, so it would have to be slightly inclined to avoid that, I expect. A mild inclination shouldn't cause any heartburn.
All that said, I'm not sure avoiding GEO is actually going to save money in the long run. A launch to an eccentric 24-hour apogee may actually not save you very much as compared to a GEO launch (I haven't actually run the calculations to see, but feel free), and going with a Molniya-like 12-hour orbit would require two or three separate launches to set up, so it's hard to imagine a way to make that work that costs less than a single launch all the way to geostationary.
For the record, I don't know much about the government/business/international aspect of satellite launches and GEO 'parking spaces', so I'm only addressing the physics of the orbit. There are probably complications involved in getting permission to use a specific orbit that I can't address.