You are correct,you would not have this problem had you put the safety on first.The safety holds the striker back in the cocked,spring compressed condition.
When you began to unscrew,you rotated the cocking piece/bolt body relationship to the "bolt locked,ok,fire"position.As there is no trigger sear in your hands,the striker went forward .The striker is forward in the cocking cam cam recess of the bolt body,so it cannot rotate.
To solve your problem,the striker...the firing pin,must be drawn back about 3/8 of an inch against the force of the spring,to the "cocked" position.Except it won't cock,as the trigger/sear are in the receiver.
Once it is drawn back,the safety will be able to rotate into the notch to hold the striker to the rear.
Look at your bolt,think about what I just told you,so you can see and understand where you are going.
Now,whether you use a vise as Gary suggested,or just hook the bench as I suggested,that rectangle block about 1/4 in wide under the striker needs to be pulled back compressing the spring.About 3/8 to 1/2 inch is how far it needs to be pulled back. Use one hand while the safety gets engaged with the other hand.Once you do that,you will be able to easily unscrew the striker/cocking piece assy.
Yes,you do have to remember that little detent button on the left side of the bolt sleeve.You found it once already.
I don't know what else to tell you.