There are a few other methods to get what you want. The first would be to put a preamp in front of the Kaiju. This will let you crank your source level up all the way (this will maximize SNR from the source, and can potentially sound a bit better) and give you a bit of extra oomph to drive the input of the Kaiju.
You could remove the 100K trim pots in the Kaiju and install a set of 1:5 input step-up transformers to boost the incoming signal, but you have to be careful about how capable your source might be in terms of driving the transformer primary. Doc B. and PJ will probably grind their teeth a little when they read this, but it's a possibility.
The other option that comes to mind is to use a higher gain tube in the Kaiju. I don't think this is a good idea, as the 5670 is a marvelous little tube, and I'm not aware of anything pin compatible that will get the job done. The amp could, however, be rewired for the 12AT7, which would give you a little extra gain (3 or 4 dB I think).
Still, going to the 8 Ohm wiring configuration is the best first step. I'd probably consider adding a preamp if that doesn't quite do the job.
-PB