It is early days yet but I think I am almost there.
I have added a small trimmer cap (T1) in parallel with C1. It gives a finer adjustment than L1.
I have also replaced the original L2 coil with a toroidal one. It has 2 windings one is thicker wire than the other and I used that as the primary.
Not sure what the full spec of it is, but it works well with any length of aerial, giving a signal better than the original L2 even when it was tuned.
But the toroidal one does not need to be tweaked, it works well with 18 inches of wire, 5 feet or wire or even better, connected to my RF earth. (which does have about a 12 foot drop down the side of the house to the earth rod)
Last night I found a new clear channel on MW 1188kHz and set L1 approximately. I adjusted T1 the new trimmer turned it off and left it for the night. This morning the frequency had drifted up about 8khz whilst the TX was turned off, possibly change in temperature in the room had caused the larger than expected change, as well as the ferrite slug settling in the core of L1. So I reset T1 without touching L1, left the TX on and when I returned just over an hour later the frequency was still reading 1188.04kHz.
Mike