Daniel,
Philip Ballister got in touch with me and thought some of the following material might help you out:
Now to address some of your specific requests:
The only thing I know of that covers 3.5 MHz up to 2.4 GHz, full duplex, for a reasonable price, is the LimeSDR. That said, other names come to mind for this class of usage, including Ettus B200 series, HackRF One, Airspy R2, and the bladeRF. Each of these doesn't meet some aspect of what you want. Either the low end of the frequency range can't be reached (B200, Airspy, bladeRF), or the device isn't full duplex (Airspy has half-duplex T/R capabilities).
I'm not sure what clock stability effect you're concerned with (frequency accuracy when tuning?), but this shouldn't be a problem with any of the above. If it is, the beauty of SDR is that you can correct for these kinds of things in software. There are likely carrier recovery / PLL tricks that should easily make sure the signal you demodulate is nicely down at zero IF, but of course the technique depends specifically on the modulation you're working with.
As for PAs, I've happily used Minicircuits components in the past. Some models that come to mind after two seconds on their website are: LZY-22+, ZHL-20W-13SW+, ZHL-100W-272+, and this is based on your frequency ranges. Note however that these aren't typically considered portable, as they all have sizable heatsinks and fans, and weigh several pounds. Also, some of these have significant output power overhead beyond your requirements, and use various power voltages, so that's something to consider.
If it was me and I was taking the show on the road, I'd get a 4U or 6U 19" rackmount chassis I can roll around, like the kind for audiovisual equipment (Gator, SKB RotoRacks, etc.), and get plates / trays that fit this very standard form factor to mount stuff like PAs, SDR, and DC PSUs. Matching PSUs with PAs and desired frequency ranges will be an engineering trade-off you'll have to consider. Plug 120VAC into a power strip in the chassis that's connected to the DC PSUs, and jack a laptop into the USB connector that hangs out of the back to connect to the SDR and do demos, it's that simple :-)
Just my $0.02
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Raj Bhattacharjea, PhD
Georgia Tech Research Institute
Information and Communications Laboratory
404.407.6622