Doors and Windows - Installing a storm door w/ no brick mould?

So I have a dilemma... I'm a new homeowner and I'd like to install a storm door on my front entrance. I purchased the door, and thought it would not be an issue as I have installed storm doors before. However, I do not have any brick mould around my front door. Instead I have 2 1/2 inch vinyl casing with a J-channel built in to it. The problem is that the casing is hollow and obviously will not support a storm door.

My first instinct is to pull the casing off and install actual brick moulding around the front door to install the storm door, but I'm wondering if this is the only way to solve my problem. Since it seems like a lot more work and there has to be an easier way...

Has anyone else ever dealt with something like this? I'm in some serious need for advice since it is supposed to SNOW next week and would like to get the storm door up this weekend.

Thanks in advance...

Can you reinforce the vinyl with angle iron, if that's the correct term, something like you see on a bed frame?

I installed a storm door on a 3 season porch. The porch was all aluminum. There was no brick face.

If you have the room and have a standard woood framed door, you might check into an "inside mount" kit. It may be available for your door.

I considered the inside mount idea, but the jam is too narrow... after doing more research I guess the official term for the vinyl casings is vinyl lineals.