You'll get the Wain Bows at the highest tier Military Development building, which I believe requires a Chamber of Lore first. (Check the building browser to be sure) Definitely don't convert it to Mannish if you want the Wain Bows!
Living the dream:
I managed to get military access from both Rhun and Khand, and assembled a stack with 2 FMs, which I later split to recruit mercenaries. This stack got most of the cav mercs and Wain Bows; the other got more Dwarven units and Catapults.
I would have had a third FM, but he was literally stuck in Erebor by 3 Dale stacks who were all crowded around, blocking the roads and ford. Very frustrating - I had to disband around 8 units of Dwarves there. I guess good policy to prevent that might be to just sit a few of your own units on those choke points.
Harad continued to do very well, storming Ithilien and taking Minas Anor and Ost-in-Agorlad before Rohan and the RK could mount a counteroffensive. On the eastern flank of the Empire, I brought my stacks down to Khand's capital just in time to see off a Haradrian siege army there, and managed to press southwest, take Caras Agar, and gift it to Khand. Harad has meanwhile lost several other settlements in the area to rebellion. Unfortunately, Khand was recently attacked by Rhun, who has destroyed Rhovanion and is in the process of doing the same to Dorwinion. (I dropped my alliance with Rhun as I want to keep gifting settlements to Khand in the Harad region... hopefully I can keep them alive.)
One of my armies is now marching on Caranbad. I'll try to take that, hold it, and develop it as my base for taking the ivory and incense provinces that border it.
Meanwhile, I have a third army marching south through Rhun and Khand. Some more Dwarven units, Wain Bows, and mercs, with 2 more FMs leading.
I'm undecided currently what to do about Rhun. Rhun is allied with most of my allies (RK, Rohan, North Rhun, etc), so if they attack me first, I'll probably lose all of those, and my FL's Authority will drop. On the other hand, if I attack Rhun preemptively, I'll lose the trade income that much sooner. Either way, losing trade with Rhun would probably be a disaster. I'm currently making around 8k per turn, but I'm sure a lot of that is due to trade from Narag-zigil, which is at this point almost entirely surrounded by Rhun.
Best case scenario would be for the RK to war with Rhun and thus give Rhun something else to do rather than get huge conquering Khand, but with Harad driving a wedge up the Anduin I don't see that happening.
And as for the South, my hope is to quickly take cities, and then see about coming to terms with Harad (ceasefire... they *might* go for it) and/or settling Khand at my back as a safe trade partner. Harad is rather dangerous with all their jav-equipped swordsmen. I'm not entirely sure what Hirelings I'll be able to train down here either.... But man, Dwarven catapults are incredibly effective!