Shy Torque,
I have had a JP5 (no tip tanks) in an inadvertent inverted spin after attempting to enter an erect spin on an up vertical line for a spin from a manoeuvre. The Aircrew Manual said that the inverted spin recovery was to centralise the controls which I did. There was very severe aileron snatching that I could not contain but it did recover after about 5 secs. A bit of research revealed that no inverted spin trial had been flown on the JP5 and the recommended recovery actions were read across from a trial in a JP4 which had tip tanks and, therefore, different roll and yaw inertia characteristics as well as different spanwise airflow at the tips plus a different nose shape.
The Hawk T1 has an inverted spin mode during which the rudder overbalances fully in-spin, and if the rudder is not centralised within the first half turn then the rudder pedal force required to centralise the rudder for recovery is about 250 - 300 lbs and very difficult to apply; fortunately it is not prone to entering this mode.
The Tucano was the first UK military aircraft to be cleared for intentional inverted spinning since, I believe, the Vampire T11 (can anyone confirm this?) and that is why we were so keen to have a single spin recovery procedure for all spin modes.