Good to see that the LPF was the cause, which logically it had to be.
Why did L5022 unsolder itself, i will give my reasoning but it needs to assume that with your newly modified 847 you enjoyed the sporadic E not only on SSB/CW but perhaps FM as well on 70 MHz.
Before going any further your reference to coils before was about L5006
which is NO longer regarded as the way to modify these sets on 70 MHz.
Your findings are relatively new, i think.
So the L5022 over heated due to resistive losses generating enough heat to melt the solder.
This is fairly common with some things i have made!
The way around this is to decrease the resistive losses in the coil by using thicker gauge wire and a coil form which is basically square ie diameter is the same as the length. This will decrease the resistive losses and hence the heating. This is of course "Q" of the coil, and for these sets i would imagine it's way<100.
The coil was never designed to handle this power on 70 MHz, where i imagine the resistive losses are higher than at 50 MHz for which it was designed for.
When you sort the coil out a small fan will aid the coil cooling.
Search on google for Marc Vlemmings it may clear up the coil in the PA as opposed to the LPF(6).
Of course you could always fit a bespoke filter and relays for 70 MHz
and switch it in from the "logic" transistor which was used to limit the power to 20 watts on 70 MHz
I think Marc quoted 100 nH for this coil.