1979 Chevy Corvette sudden overheating problem

If you are seeing steam in the radiator, then you probably have a leak. Best thing to do is to when it starts to overheat, shut engine off and feel around aradiator. It should be the same temp or about all over. It should not have any cold spots if it does your rad is shot, it probably is anyhow. If there is steam leaking out do not even attempt this as you can get badly burned. It could be your hoses as you say they are soft. A way to look at those is while the car is running, rev it and look at the bottom hose, it may be sucking together and not allowing water to go through it. It would be a great idea to replace your hoses as well due to them being soft anyhow.