Thanks for the feedback and excellent screenshots.. that helps me see what is happening.
The change in IP fixed one problem.. it means the satellite system is using 10.x.x.x address somewhere in the system.. but interestingly you are actually getting a special IP which is not public but likely CGNAT.
As a test you could try doing a traceroute from the terminal to any normal web address.. e.g. google public dns like 8.8.8.8 and see what you come up with. I would expect some 10.x.x.x numbers in there.
traceroute 8.8.8.8
traceroute to 8.8.8.8 (8.8.8.8), 64 hops max, 52 byte packets
1 rt-ac3200-82f0 (192.168.2.254) 1.837 ms 0.932 ms 1.040 ms
2 melbvoc-lns12.mel.eftel.com.au (203.123.68.185) 17.571 ms 17.784 ms 17.745 ms
3 po-1-353.core1.mel.eftel.com.au (203.123.68.193) 17.927 ms 18.200 ms 17.613 ms
4 203.123.69.134 (203.123.69.134) 18.702 ms 19.230 ms 18.841 ms
5 233.1.2.123.network.m2core.net.au (123.2.1.233) 29.813 ms 29.898 ms 30.311 ms
6 74.125.52.10 (74.125.52.10) 30.598 ms 31.620 ms 31.537 ms
7 108.170.247.33 (108.170.247.33) 31.130 ms
108.170.247.81 (108.170.247.81) 31.326 ms
108.170.247.49 (108.170.247.49) 31.451 ms
8 216.239.41.1 (216.239.41.1) 30.514 ms
216.239.41.189 (216.239.41.189) 82.072 ms
66.249.95.51 (66.249.95.51) 31.713 ms
9 google-public-dns-a.google.com (8.8.8.8) 126.147 ms 29.250 ms 136.867 ms
The problem with high latency links is the way it interacts with other links like wireless which share bandwidth and can also be high latency.
Apple does not give us anyway to fix packet size in wireless.. but the usual solution to this is reduction of packet size.
The issues seem more than just .7 of a second and is unacceptable on things like WIFI assist calls, Skype, Web X, FaceTime etc.
You really need hard wired connections for anything interactive on your end.. wifi is just going to work terribly. And btw that is the case with even a double hop wireless system.
For example you are using double hop wireless.. so if you are trying to make a call over wifi from your phone.. and the phone connects to one of the express instead of the extreme.. the connection will become near unusable. I found this out myself the hard way. If you at least remove the double hop this will help. ie the phone must connect to the airport extreme.. never the express.
In the end you could try with a wireless router that allows pro level access to reduce packet size.. and you must eliminate double hop wireless.
However I think the satellite is probably just not going to work well enough for this.
If you can afford it.. the best solution is to keep the DSL network going.. and use it specifically for any interactive calls you are going to use. Keep the satellite for data streams.