Is the preamp circuit really that different between versions? I would think they'd be close either way. Can you see the oscillations on the output, without any other signals applied? If so, try unplugging the input cable at J1, eliminating any input signal and the cable capacitance, and see if it becomes (at least marginally) stable.
I haven't used or seen the insides of my 11729C in years, so don't recall the looks and accessibility of the modules. Can the preamp be opened up and set up for operation while open, and out in the open for access? If so, then you can use the old pencil trick and poke around the hot nodes to find the sensitive spots. 27 MHz seems rather low for one of these stages to oscillate at - you'd expect something at VHF or up. So, it would likely be due to the preamp's LF feedback loop instability, or in the power amp stage that is much slower. Q6 could maybe use a bead on its base too.
Another possibility is that there are actually two VHF oscillations going on, and the 27 MHz is just one of the mixing products that's in-band for the overall amplifier. If you have a spectrum analyzer handy, try looking at the output, but at way higher frequencies and sensitivities. If nothing shows at the output, try looking at the input, where you may have closer access to any VHF stuff going on in the preamp.
Before digging too deep, it would be good to do a quick check through the stages to be sure the DC bias levels make sense.
You are right to question the PS bypassing arrangement, and try adding some HF bypass caps. However, if these electrolytics are tantalum type (most likely), then they should have good performance even at RF, so the need for extra bypassing is greatly reduced. Worth checking though, just in case.
BTW the schematic I'm looking at says it's A6A1 low noise amplifier board assembly (11729-60009).
Good luck.
Ed
