Someone will no doubt say that this isn't realistic
It probably isnt!
What did you do during your simulation? I suspect you reduced the power to idle.
There is a BIG difference in a real engine failure. Has the prop siezed? Is it windmilling? Have you still got take off flap selected?
Trim will be affected by a stopped or seized engine (much more nose down... meaning lots of nose up trim..which may run out).
By throttling back to idle you still have a little residual power (put simply somewhat like feathering) which reduces drag. It can be nothing like the real thing!
Try stopping the engine at altitude with the mixture control, then switch off both mags. You may be quite surprised at the result, and thats probably without the prop actually stopped!