L5 yes it does cutout with the configuration you presented. I assume you have No 2 engine running?
On the ground:
The packs operate in either AUTO or HIGH. In AUTO the pack valve will modulate a lower VOLUME of air than HIGH (normal pack flow rate) from the bleed duct. For pack-loading relief the recirc fan will make up extra air going into the mix manifold. This air is derived from the cabin via the forward cargo bay which in theory is supposed to be coolish. Because its a fan its pushing air through the system which is why it feels better. I agree its a dumb system in high OATs.
When you select HIGH you are restoring normal pack flow rate. What your probabley feeling is a rush of normal VOLUME pack air. The recirc fan is of no value anymore. Indeed if the recirc was operating youd have coolish air mixing with full cold pack air, which you dont want.
The switching you describe doesnt fool the recirc logic in this case unfortunatley.