Why doesn't my cascode circuit work?
The circuit is not a Cascode. A normal cascode would be a common Gate stage stacked on top of a common Source stage. This is done to get high voltage gain from the common Gate (top) stage while eliminating the Miller multiplication of \$C_{\text{gd}}\$ of the top FET, and reducing the Miller effect of the lower FET \$C_{\text{gd}}\$ by the voltage gain of the top stage. Of course, the gain of the top stage is taken from the Drain of top FET (from between the Drain and some resistance, either real or synthetic, connected to the bias voltage). But, you don't have that here, so there is no voltage gain from the top stage. What you have seems more like a Source follower stacked on top of a common Source, but that's not right either. I don't know what you would call this topology. 

Now, the first circuit you talked about where the Drain of the (single) lower FET was hooked directly to the bias voltage would have been a Source follower. A Source follower presents a relatively low capacitive impedance of just \$C_{\text{gd}}\$ at the Gate (that the OpAmp must drive). With bias voltage of 25V, the \$C_{\text{gd}}\$ of the IRL1004 is about 320pF, and the OPA227 can probably handle it OK. 

But, if some impedance is placed in the Drain leg of the lower FET (between the FET and bias voltage), \$C_{\text{gd}}\$ is multiplied by that impedance and FET transconductance (\$g_{\text{fs}}\$). And at these voltages, the IRL1004 \$g_{\text{fs}}\$ ~ 50S. So, for example if the lower FET had a 1 Ohm impedance in series with the Drain, capacitance seen at the Gate would be about 16000pF, which is a lot for the OpAmp to handle. 

But wait there's more. You didn't put a resistor in series with the lower FET Drain. The impedance you put in series with the Drain of the lower FET is another FET. So, \$C_{\text{gd}}\$ will present itself at the Gate of the lower FET multiplied by transconductance of both the lower FET and the upper FET and some mystery FET impedance. Whatever it is will be even more than 16000pF. 

Also, since these FETs have such low on resistance, if they are turned on, yes they will short out the 25V bias supply.