Almost 80% of your arguments are invalid
You're saying "Healthy Nagato' not SPOP, so he can't just beat 1 path at a time.
You can't use a Spacetime barrier on CT, it's pure gravitational pull, it doesn't have a form, but let's assume he can.
As soon as Minato tries to use a contract seal, he's touching Nagato, Nagato then Holds him in place with a few arms ( stronger than Bee+Naruto ) Drains his chakra and or pulls his soul out, so Contract seals won't work.
Nagato VS Naruto was kind of biased, As soon as Nagato had Naruto it was over, he could have drained him clean right then if he wanted to, or stabbed him, immobilizing him.
Nagato Counters FTG with ST/CT, he can send all his kunai to where ever he likes, and if CT would destroy any seals on things. Space time takes handsigns, and a small prep time, easily interrupted by Summons,Rockets, Deva abilities or just the CT itself.
ST isn't a great choice here, but he can use the other one that drags minato towards him, Then drain his chakra, his soul or just stab him....
It took Nagato seconds to drain 8tail cloak from bee.
Nagato wins mid dif.