Glamdring, LTA vehicles are not as vulnerable as you think. In the North Atlantic during WWII, our blimps were in on the kill of many U boats, yet only one airship was shot down. And with modern design and materials, a blimp could be made very damage-tolerant. And relatively cheap, too. If we had a couple hundred of them, 99 out of 100 banana republics would empty their SAM arsenals without clearing the sky of our airships.
A few years ago, I would have said that our best bet for fleet ASW was LA class attack subs. But now, the Navy is claiming that the Russian Akulas are as quiet as ours, which probably means we'd have to use active sonar (i.e. hull-mounted and towed sonar from destroyers as well as sonobuoys). The airships would do a good job of dropping sonobuoys and prosecuting contacts, since they have quasi-infinite loiter time. The USN is apparently looking into this right now, though the odds of funding are probably low.
But we're still lacking high-speed transport ships in the quantity to move serious ground forces. We don't have to develop a damn thing, we just need to start building hulls from existing designs. I guess you could claim that our combat capability is not defined by how fast we can put a light infantry division on the desired spot on the map, but how fast we can deliver one mech inf division and one armored division to support the "speedbump forces."