I think it unlikely that it is a head gasket problem. Does it drive OK? Firing on all 8? Can you do a compression test? Any sign of coolant in the engine oil? Any sign of oil in the coolant? Is it running particularly hot?
With the cap off, I would expect the coolant to spill over due to the water pump action after the thermostat has opened. If you don't have a thermostat, I guess it would do this pretty much straight away, especially as you don't seem to have an easy way to bleed the system.
It sounds like your best plan is to do as you say, make the trip to Silverstone with a 'new' motor planned for the near future. I really can't offer specialist advice on the FE motors as I only know small-block Windsors - I seem to remember the 427 has the thermostat housing built into the header tank, but may be wrong on that. Either way, if it drives OK and doesn't show signs of serious overheating, you should be OK. Carry some water to top up, and if it starts to get very hot switch off in the S'stone queues!
I'll be with the 289 Register with my 289, which regularly runs at between 90-105°C, especially in these temperatures. I'm running Evans so it's not going to boil and has not shown any signs of distress thus far, so fingers crossed.
What pressure rating cap are you using? Coolant expands when hot and you are probably getting overflow at switch-off due to the spike in temperature caused by the water pump ceasing to turn. I have a catch tank for the coolant overflow, which sucks back into the system as it cools down.
Are you filling it right up each time? It may be that the system wants to run with the quantity of coolant left after it's overflowed. You may need to just leave it as it is, but carry water just in case. I'd still like to see a thermostat in there somehow, though - maybe in the side-oiler!