Hi Alex,
The 'standard' 869.5MHz PilotAware antennas - (the ones supplied to screw directly onto Rosetta) are technically known as 'Sleeve Dipoles'. You can see an excellent description of how these are designed and constructed in the first part of this video...
https://www.youtube.com/watch?v=wcho1gJ2xEQ (up to about 4mins 20 secs).
There is technically nothing to stop you running a sleeve dipole on an SMA male to SMA female 'extension cable' of appropriate length - remembering that the shorter the cable, the less potential signal loss. They usually work fine in that configuration as they don't need a ground plane. Just make sure the cable you buy is good quality for the frequency we are using and that the connectors
are SMA - not 'reverse polarity' RP-SMA - which has the centre pin in the wrong connector, and try to mount the antenna out in the clear away from for example metal window or door frames.
I've never taken one of the 'standard' Rosetta 1090MHz antennas apart yet, but from their length, I suspect they are simply tuned 1/4 wave monopoles. The reason they are not 'advertised' as compatible with the Classic, is that - as you know - the standard Classic 1090 antenna has it's own cable, terminated in an MCX male plug, which plugs directly into the dongle, whereas on the Rosetta the antenna mounts directly on the case onto one end of an installed SMA to MCX pigtail - the other end of which is already plugged into the dongle. Again, there is nothing to stop you using a Rosetta 1090MHz antenna onto an SMA female to SMA male 'extension' with your 'Classic' then adding an SMA female to MCX male adaptor on the end of the cable to plug into the 1090 dongle. Or you could of course use an SMA female to MCX male cable if you can find one.
Having said all that, remind me what type of aircraft you are flying? If you are changing your antenna setup anyway, have you considered upgrading to
external antennas? I did that quite a while back on my flexwing and as a result am seeing vastly improved coverage and range from my setup over all previous antenna options.
Definitely worth thinking about.
Best Regards
Peter