But here is an old idea. The switch shorts out the coil as you go higher in frequency, eliminating your concern.
Yes, that is exactly what I was trying to describe but didn't have the picture you posted.
Note the extra loading cap which automatically comes in at the lowest band.
Now that's a neat trick using a one-pole switch! Wish I'd thought of it myself.
I will implement that once I locate a suitable rotary switch. My loading cap is a vacuum variable (8-1000 pf) and it may take even more than 1000 pf additional...
thanks for the schematic
-Charles