@simon___1 those solder pads still look good. All you would need is to replace the coax connector by soldering a new one to the logic board. Remember, that this is a bit tricky for anybody new to this, but anyone that has done board repairs can solder those for you. The replacement connector would be a 20449-0001E-03 IPEX RF MHF CONNECTOR available at places [https://www.chip1stop.com/USA/en/product/detail?partId=IPEX-0000233|like this] and many others.
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=== Update (11/26/2020) ===
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You do need a replacement since your connector has failed. Sure you could try and solder the outside ring to it. You will never know how long it lasts and there will always be doubt about it. Since you already have it all apart etc, spend the few $ and fix it properly. That of course are only my 2 cents.
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The center pin you are referring to actually connects to pin 1. So with a new connector you will not have to worry about it
@simon___1 those solder pads still look good. All you would need is to replace the coax connector by soldering a new one to the logic board. Remember, that this is a bit tricky for anybody new to this, but anyone that has done board repairs can solder those for you. The replacement connector would be a 20449-0001E-03 IPEX RF MHF CONNECTOR available at places [https://www.chip1stop.com/USA/en/product/detail?partId=IPEX-0000233|like this] and many others.