Hi, just one point right now as it happened to me as well:
Be careful with the connectors. They are pretty sensitive. While pluggin in a wrong cable in mine I actually bent the connector itself upward, but it didn’t damage the connection traces… so I had luck and it was a good reminder. They are pretty fragile…
About your connection problems. I do use some cheap chinese radios. You get them around 20Euro. These have a fitting connector, but as far as I remember I had problems fitting these in my original 3DR pixhawk. I could press them in with force and they stay there. Well, as I mentioned my experience above, I would clearly advise you not to do so in this case
3DR Pixhawk uses Hirose connectors but a lot of clone manufacturers use JST connectors. They look very similar, but they differ a bit on the design.
When you use original 3DR radios, that would mean you should have Hirose connectors.
Maybe Reach uses JST connectors as well…so that could be an explanation. Maybe someone from the team can give you a hint.