CAUTION: The below post describes an advanced loading technique that may result in increased pressures in revolvers. PROCEED at your own risk. Neither the writer, The Firing Line, nor the staff of TFL assume any liability for any damage or injury resulting from use of this information.
This is an advanced reloading technique, and you have to seat the bullet out. Of course, it's possible to make a heavy .38 special charge, but you risk losing your revolver. However, if you seat the bullet out to .357 length, then there is room under the bullet for what you want to do. We all know that the .38 Special and the .357 magnum are virtually identical except for case length. So, if you seat the bullet out to .357 length, you've got the room under the powder charge that you need.
The old Lyman 358156 has two crimp grooves. It is a Ray Thompson design and was made especially for what you're talking about. For regular loads, either .357 or .38, you loaded as usual and crimped in the top crimp groove. However, when you didn't have .357 brass, you loaded the .357 charge into the .38 Special case and seated the bullet to .357 length and crimped in the lower crimp groove.
This technique, as all advanced reloading techniques, required that you mark your box of ammo so that you didn't inadvertently load it in a .38 Special cylinder. Depending on the length of the cylinder, some .38 specials would let these loads chamber, some wouldn't.
I've used the same technique myself during a local shortage of .357 brass. I use the Lee TL358-158, which is a 158 grain semi-wadcutter with the micro grooves. I simply prep the brass as usual and load to the .357 OAL. Then crimp into one of the lube grooves. No problem at all.
Again, this is an advanced technique that requires you to seat the bullet out farther than normal. Proceed at your own discretion.