My main run is 1 1/4" PVC.
If I reduce straight to a 3/4", will that blow out the joints?
Should I transition to 1", then to 3/4"?
The water source is well, with good pressure.
I believe a direct transition, properly cemented, at normal water pressures, should hold just fine.
The downside to a gradual reduction as you described is the exact concern you put into your question - joints.
Your gradual transition idea will give more opportunities for joint failure simply because there are more involved.
PVC cement often surprises me how strong it can be.
So my recommendation is that you try a direct transition first. In other words, don't try to solve a problem until you know it exists. Make sense?
The pressure in the 1-1/4" pipe is EXACTLY THE SAME as the pressure in the 3/4" pipe. That is true whether you stick 15 transitions or one in there.
You evidently made a bad joint - perhaps the pipe was wet, perhaps you used old glue that was going bad, perhaps you failed to twist and shove and hold in for a minute.
If there will be a problem with ensuring that the pipe is dry, there is special cement for that.
Old glue is a frightfully common error - if it's thickened in the can, you are wasting your time using it. New glue is cheap.
I used to be rather casual about doing PVC joints, until it bit me (leaky joints, had to re-do.) I now always use cleaner, then primer, then glue, following the instructions closely. I try to make sure that I get a quarter turn while pushing the pipe home, and I hold it in place firmly. I have not been bitten (had to re-do for leaks) in a while.