Ahriman
Tyrant
Archer units look far superior to the infantry units. Strength 9/12 is waaaay better than strength 12, particularly when the latter requires a strategic resource and the former doesn't.
I really recommend that you make strategic resources uncommon-to-rare and make the units that require them into elites.
A way to make the recon line more interesting might be to make them actual skirmishers, with a 1-tile low strength ranged attack. That might work better than invisibility, which the AI doesn't tend to handle well.
You might also consider having the elephants have the chariot penalty, where entering rough terrain ends their turn. That might help balance them.
You could also consider a spearman/militia/cannon fodder line. I would worry a bit about having recon units as the only resourceless unit line.
I also think that the way Civ5 handles strategic resources might not be well suited to this kind of FFH-style approach.
In Civ4, a single copy of a resource was enough to support an unlimited number of units, so with a single resource you could gain great profit from pursuing a particular tech line.
In Civ5, the strategic resources enable a very different kind of system, they enable a combined arms approach, where you can only have a few of a particular type, limited by that resource. This works well in a narrow-long tech tree rather than a short-broad tech tree.
Another approach would be to have a core set of expensive "tactics" techs, which governed the main set of military advancement (warrior code/tactics/warfare/conquest or something similar) and provided a weak generic unit, and then have the various military techs be cheaper but require a sufficient level of advancement down the tactics line. This might mean that it would still be worth getting archery techs even if you had only a handful of yew resources available, it would still be worth getting the archery techs, because their marginal cost is modest.
The only other ways I can see things working is either by having so many strategic resources that resource availability isn't really binding (this is how vanilla tends to work for most resources) or by concentrating resources in particular regions so that region X has lots of horses but not much else and region Y has lots of Yew but not much else. But this forces a strong geographic determinism, and doesn't leave the player with much choice of strategy, since they're forced to research whatever resource they have locally.
I really recommend that you make strategic resources uncommon-to-rare and make the units that require them into elites.
A way to make the recon line more interesting might be to make them actual skirmishers, with a 1-tile low strength ranged attack. That might work better than invisibility, which the AI doesn't tend to handle well.
You might also consider having the elephants have the chariot penalty, where entering rough terrain ends their turn. That might help balance them.
You could also consider a spearman/militia/cannon fodder line. I would worry a bit about having recon units as the only resourceless unit line.
I also think that the way Civ5 handles strategic resources might not be well suited to this kind of FFH-style approach.
In Civ4, a single copy of a resource was enough to support an unlimited number of units, so with a single resource you could gain great profit from pursuing a particular tech line.
In Civ5, the strategic resources enable a very different kind of system, they enable a combined arms approach, where you can only have a few of a particular type, limited by that resource. This works well in a narrow-long tech tree rather than a short-broad tech tree.
Another approach would be to have a core set of expensive "tactics" techs, which governed the main set of military advancement (warrior code/tactics/warfare/conquest or something similar) and provided a weak generic unit, and then have the various military techs be cheaper but require a sufficient level of advancement down the tactics line. This might mean that it would still be worth getting archery techs even if you had only a handful of yew resources available, it would still be worth getting the archery techs, because their marginal cost is modest.
The only other ways I can see things working is either by having so many strategic resources that resource availability isn't really binding (this is how vanilla tends to work for most resources) or by concentrating resources in particular regions so that region X has lots of horses but not much else and region Y has lots of Yew but not much else. But this forces a strong geographic determinism, and doesn't leave the player with much choice of strategy, since they're forced to research whatever resource they have locally.