Sorry about your oven/cake issue, I had similar problems long time ago when I installed a new wall oven. The first thing I did was to buy a Taylor oven thermoteter, it turned out the oven is always 20/25 degrees lower than the setting (it has a digital control panel).
This pretty much addressed all the baking issues I had.
Relative to your cake sanking on the middle when using a convection oven... What kind of mold are you using? Sometimes non-stick produce funny results, like premature browning perhaps you need to bake using a thicker mold like ceramic (that will difuse the heat better) or a bain marie on the convection oven since is powerful enough to bake the outside faster than the inside. And just to make sure the temperature is not an issue, use a thermoteter too in the convection oven.
I hope these comments helped you.
"Tell me what you eat, and I will tell you what you are" Anthelme Brillat-Savarin