Tagger,
Sorry to be such a late-comer but am compelled to reply, hoping not too late.
You said on Jan 8 "I agree...the other alternative is the increase the diameter of the spline to closely match the diameter of the shaft (Ø6"

. This would involve changing another component of the design to match the increase spline diameter."
If you can do this, the gain in torsional resistance, fatigue resistance, reduction of spline root stress, etc will be so dramatic that it pales all the other suggested fixes by a HUGE factor. Compare the Polar section modulus of 4.7 vs 6. It is a cubic function and therefore you DOUBLE the torsional strength. You said the 4.7 will handle the torsional stress but you need to increase the endurance limit.
If this is still an alternative, DO IT because this will save you oooooodles of headaches trying all these different suggestions. Not that there is anything wrong with the suggestons if you have the luxury of "trying them".
We had a similar "design" problem (torsion and bending with splines of 4340) and tried every single suggestion posed here-plus some-except for the astroloy version because instead we finally used maraging steel which doubled the fatigue life. This bought us some time, several years in fact (even though maraging shafts were still fatigueing in as short as 4-6 months in sever applications) to allow us to slowly introduce a new design of a complex gear case including a planetary that had to grow in order to grow the diameter of THE splined shaft that passes thru the sun gear. Our original design did not allow for an earlier unknown reverse torsional load on repeated start-ups. In other words it was a geometry problem such as yours.
For example: Let's say you neck down the shaft at the end of the splines. This could possibly give you a high enough stess at the necked down region to still give you a marginal endurance limit at that section.
And yes you can nitride maraging steel but why use exotic materials as TVP states when more practical solutions are available. A maraging shaft that size would probably cost upwards of $1,500 just for material assuming it is only a few feet long.
Jesus is THE life,
Leonard