If you've already a 3.42 rear axle, and the 8L90E, you really don't need to step up to more than 3.73.
Multiply your 3.42 rear axle, by 8L90E's 1st gear.
My DESIRED rear axle would be 4.10, times 4L60E's 3.06 = 12.54, for a frame of reference.
Do the same for 8L90E's final overdrive gear of 0.652.
For me, 4.10 times 0.7 = 2.87. Effectively I'd be improving city MpG to sacrifice highway MpG.
That's why I'd prefer 3.90 - which I don't think they make? - to 4.10, since I don't tow or offroad.
3.42 * 4.56 = 15.59 Your present 1st gear
3.73 * 4.56 = 17.01 Your 1st gear with 3.73 rear axle
4.56 * 4.56 = 20.79 This may break something, and make 1st gear too short, might as well be a seven speed
You REALLY don't NEED any more 1st gear torque multiplication than 3.73 will provide.
3.42 * 0.652 = 2.23
3.73 * 0.652 = 2.43
3.73 might actually save fuel on the highway, unless you enjoy speeding over 70MpH (as I do).
4.56 * 0.652 = 2.97
4.56 won't save any fuel on the highway (nor in the metro / urban).
If you want more axle than 3.73, 4.10 would be more than enough.
For best results, tune your ecm & tcm for the gear change, especially to improve the transmission's personality.