Hi Dave,
Have you read these two documents:
http://www.pilotaware.com/wp-content/uploads/2016/10/PilotAware-Antennas.pdfhttp://www.pilotaware.com/wp-content/uploads/2016/12/161205-Permanent-Installation.pdfYes, fitting your antennas as proposed should give excellent results.
For very long coax runs we normally suggest RG8X, which is slightly thinner than RG8, but SMA connectors for RG8X are difficult to obtain - only available from the USA and it won't be particularly easy to fit in an aircraft.
At the sort of length you are talking about, loss won't be too critical, especially for the 1090MHz receive side, but as you are obviously aware you need to be more careful for the P3i side due to its much lower power levels. PilotAware Hardware
www.pilotawarehardware.com sell pre-assembled
3 metre extensions with SMA connectors. These use a fairly thin coax, which is fine at that length and being flexible, easy to route. I'm not sure what the coax 'type' it is but Dave, who runs PilotAware Hardware should be able to tell you via the Contact link on the site. Replacement SMA connectors for that type of coax are fairly readily available on eBay if you need/want to shorten it. Remember you will also need a crimping tool, such as
https://www.maplin.co.uk/p/coaxial-connector-crimping-tool-a38qw to attach them.
With regard to antennas, you can use PilotAware tuned monopole whips (tuned to 869MHz) for
both frequencies (they are close enough for 1090MHz receive due to the high strength of the signals), though you need to make sure they are carefully waterproofed at the connection to the coax connector and they MUST be fitted to metal bodywork or with a suitable metal ground plane (as described in the Permanent Installation Document). Several users get good results using these antennas. Other antennas specifically designed for external use on aircraft at 1090MHz and 868MHz (Flarm) are of course available but at much higher cost.
Hope this helps.
Regards
Peter