feedback techniques
I dont think the problem is related to base-collector
resistance. 6MOhm Rmu is toooo low for a real device. It might be related to DC setup of your simulation. When you say shorting the input,
you have to keep the DC signal level but remove
the AC component. For proper operation in AC,
you have to put 100mV DC voltage at the input of the amplifier, this will force the positive terminal of the resisitor to be equal to 100mV, hence you will bias your BJT with 100m/4K, 25uA collector current.
Your collector voltage should be of course couple of hundered milivolt above base voltage to assure forward active region operation, so you should choose you collector voltage arround 0.8-1V. Then,
the output resistance is defined as small signal
(that means, if you choose collector bias voltage 1V, your output reistance is not 1V/25uA (bias current))
To measure small signal resistance you have to apply a small signal AC signal (choose a magnitude that guarantee VCB>0) and you have to measure the current flowing through.