I have been pondering your problem.
Basically you are correct, that system does need to be three way and not two, and needs tri-amping.
I have modelled that woofer, and actually it is a typical pro woofer with high sensitivity and low Qts. So it has little bass output unless the low end is pulled up with horn loading. But that would be too large an enclosure domestically.
I have modelled your 2226H driver, and it has little bass. The optimum enclosure size is actually 2.5 cu.ft. A pdf. of the model is attached.
So it needs a good sub crossed in at 100 Hz. This is pretty typical for pro drivers like that.
You horn is a midrange horn and needs crossing over to an HF horn at 6KHz.
This horn would do the trick.
You would have to pick a JBL compression driver for it.
So you would need another two channel power amp for the HF section. 50 to 100 watts per channel would be adequate.
After doing the design, 800 Hz is actually the optimal crossover point for the 2226H drivers. So a pair of Shure SR 106 crossover would be ideal and have ideal slopes for the drivers you have.
Then you could use the high pass section of your Rane unit for the HF horns. Those mid horns roll off ideally at 6KHz so, you don't need to roll them off.
I gather this is not your high end system, but it could be. You already have most of the ingredients for a high performing reference system. So, if you are up to it, it would be a highly worthwhile endeavor.