This may be totally off the wall, but here goes.
It seems to me that the main problem with the NAT scene is the lack of interest among the rank and file. This is because, unless you have a NAT player, you have no interest - financial or otherwise - in the performance of the NAT team.
I would therefore suggest that you go in the totally opposite direction to ash's suggestion of no exp, no compensation, no unavailability. As well as all these things, if a NAT team does well every club in that country receives a small amount of money. Just as, for example, the ECB receives a huge amount of revenue in relation to the England international side, and distributes that money down to the major counties, minor counties and grass-roots.
Before you roll your eyes and stop reading, consider it. First, I'm not talking about huge amounts of money - I'll get on to the sort of quantum shortly. What the NAT set-up does not currently have, in any way shape for form, is a financial structure. And yet, NAT matches do have nominal "attendances", which have no relevance to anything whatsoever.
Imagine this:
- each NAT side has a supporter mood, which goes up or down at the end of each tour (i'll deal with WC separately later)
- each match has an attendance (as currently) and a TV audience (new concept)
- the supporter mood of the two nations has limited effect on the attendance (tend to be the hardcore supporters), but a huge impact on the TV audience
- the NAT team "earns" a set amount for each ticket sold, and a different amount for each TV spectator
- the revenue earned by the NAT team is split amongst ALL the human-controlled clubs playing in that country.
That is very broad brush, and I don't propose to go into more details at this stage on how you could calculate the prices etc to ensure that the money coming into the system was acceptably small so that it didn't screw up the economy, but enough to ensure clubs (especially the lower league clubs, where there is almost universal apathy) cared about their NAT team. If people are interested in the idea generally, I do have some thoughts on this.
But that's the point - if the amount of money coming into your club coffers during a season was affected by the performance of your NAT team, you damn well would care what was going on at that level. You'd scrutinise selections, you'd follow matches, you'd care about the elections - in fact, you'd care generally.
If you achieve that, I don't think it much matters whether you have tours or leagues. People would care about NAT matches, and that would be the main thing.

- 
Manager of the

Supporter of Zimbabwe!