Here another vote for Lord of the Rings!
We use it frequently and think it works very well for our late 15th c games.
In the comments to our latest AAR (found here
http://northern-wargaming.blogspot.se/2013/04/aar-sanctuary-15th-century-skirmish.html) I explained in a bit more detail on how we use LotR for our games.
The rules we use are Lord of the Rings Strategy Battle Game that have models bases individually (i e for large skrimishes) and not the War of the Rings rule set that in effect use multibased "companies" with eight figures on a base. We use the older version and hasn't bothered to buy the Hobbit version (that as far as I know have some alterations on monsters etc).
And quick a word on the rules themselves. In my view it is a bit different from the ususal GW game mechanics. For instance it uses a system of "priority" i e who goes first each turn. You can override that given turn sequence by using a limited amount of "heroic actions". That system, that isn't used in for instance Mordheim or Necromunda (the latter being an exellent game though) although simple encourage and reward tactical gaming. Great fun!
Depending on how you compose your forces you can use very few models (like "the fellowship") or put together quite large forces.
Again using our latest game as an example here are pictures of the two opposing forces we had on the table. It isn't a problem to use much larger forces aswell - including the numbers you mentioned.


Happy gaming!
/Mattias