I heard back from Stefan at SR-Systems today. He said that if I replaced the MMIC on the minimod with a GVA 84+, and the bias inductor with a 600Ω 3A ferrite bead, that would boost the output by 12 dB. That would be enough, I think, to get us at or near 0 dBm, at least as measured by my spectrum analyzer (Stefan says I should actually expect to get -1 dBm now and close to 10 dBm after replacing the MMIC, but I think he's measuring the power by having the board transmit a CW carrier rather than measuring the power of the actual modulated digital signal).
I've gone ahead and ordered one of those MMICs. I'm not confident enough of my surface mount soldering techniques to work on a kilo-Euro worth of equipment, but I have some hopes that I'll be able to enlist someone in the hardware lab at the office to help me.
I also hope that the hardware lab can spare the ferrite bead. I think it's silly to try and order a single quantity surface mount component mail order. I bought a 20 dB attenuator in the same order as the single MMIC just to make the shipping costs worthwhile. With the attenuator, I should be able to run the output of my amp directly into the SA for power measurements and stuff (the SA can take up to 30 dBm - 1 watt - of input power).