Charlie,
Your thinking is sound.
Important question: What type of ADS-B out system are you using? I ask this to get the belly antenna count right (and keep my advice from turning your belly into a porcupine of transponder antennas).
I assume your Stratux is like the others I have where there are two plastic stick antennas on the side, one for UAT 978 Mhz and another for 1090 Mhz.
I recently installed a Stratux hidden behind the panel in a friend's 4-seat legacy aircraft. At the same time I installed a GDL 82 to interface with his existing Garmin GTX Mode C transponder. So my belly antenna transponder-style antenna count from this was 3. Two for the Stratux and the original transponder antenna since the GDL 82 uses the original in conjunction with the original transponder unit. If you wanted to hide your Stratux away you too could mount it behind the panel or even aft of the baggage area or similar.
Specific to the Stratux: I installed two new Deltapop shark fin antennas on the belly, one UAT (978) and one transponder (1090). Ball and stick type antennas would work too but were not appropriate as this was a fast airplane where the drag is much lower with a shark fin profile vs the round ball and stick (and amazingly so for aircraft over 140 mph):
So paying attention to which antenna was which frequency type I ran double-shielded RG316 coax from each of these to the corresponding Stratux antenna connector on the unit. You can see which connector is which frequency when you open the Stratux box or do a test where you swap the original portable antennas and check the reception levels from the unit's IP address as outlined in Stratux instructions. I color coded the coax end connectors and component connectors with colored electrcians tape on each end so the next person wouldn't criss-cross them. The two new shark fins were installed on the aft belly on the centerline separated 8 inches on center "in trail". That was a good location to keep them at least a meter from any comm and the original transponder antenna. The double-shielded RG 316 coax I used for this has the same small diameter as the stuff that comes on Garmin's portable unit GPS pucks. Except Garmin uses RG 174 which isn't as good as my double-shielded RG 316, which has attenuation loss per foot very similar to RG 400. It's very easy to route being so thin. And light. I have strippers and connectors for RG 316 so I can install SMA, BNC, TNC connectors to it. For MCX installations I use the commercially available pigtails found online (similar to the one uAvionix ships with it's EchoUAT unit). You could skip all that specialty stuff and just use RG 400 per industry norm. There are SMA female and male connectors available for RG 400 and I would encourage the crimp type or 90 degree type where only one small solder joint is required. Or skip that too and get an adapter for conventional BNCs on eBay, the ones with the pigtails on them so as not to over-stress the Stratux connectors:
Since the Stratux wasn't exposed to the sky it's GPS signal had to be addressed. So to complete the picture I removed the USB GPS chip/antenna module from inside the Stratux and replaced it with a Vk-162 external USB puck receiver/antenna I bought online. This GPS puck was mounted to the glare shield with it's USB plug inserted into the Stratux in the same USB hub where I removed the original GPS module. Here is what the new Vk-162 GPS puck receiver looks like:
If you do mount the unit somewhere keep in mind it's orientation. Most Stratux units have an arrow on them showing which way is forward for the built-in attitude sensors. However, you can easily change this direction by re-setting it within it's IP address while standing it on end downward on whichever end is aft (or forward or something like that). Look it up online. It's easier than I can describe here.
And finally to power the Stratux get a micro USB 12 volt power cable with built-in 5V transformer hardwire power cord:
Too much information here probably.