I think what I'd rather do is simply break the connection from the 45 grid to ground and make a connection to the input tube plate using the time delay switch. So, a 100K resistor to ground from the grid on warmup, then the switch fires, breaks the connection to the 100K resistor and makes the connection to the input tube plate.
Could you use a PSU B+ time delay like you do in your other direct-coupled builds like airmid, rather than this switch between the two tubes?