Good morning, David;
John Nikon F has exactly the same thought I did in thinking what is the most likely cause of your light meter optimism. There are a couple of other ways to compensate also, but they do involve the use of a different battery. As John said, the problem is the difference in electrical characteristics of the original PX-625 Mercury Battery. One simple "work-around" is to use a "Wein Cell" or "Air Battery" of the type often used with hearing aids. Some people will use an O-ring around the outside of the Wein cell to hold it centered in the battery compartment. The only criticism of the Wein cell is its relatively short life in this use; only months instead of a year or so. Some people have reported being able to extend the battery life by putting a piece of a plastic tape over the air hole on the side of the Wein Cell when it is not in use.
Another way is to use a Silver-Oxide or Ag-O battery such as the 357 or the S-76 or similar cell with one of those O-rings around it to help hold it in the battery compartment as a stable source of the power to run the light meter, but at 1.55 VDC, the Ag-O battery will be off calibration just like your Alkaline Battery, but at least it is a stable voltage source that does not drop and change calibration over its life as with the Alkaline Battery, but there is a relatively simple modification to your camera that your camera repair guy can make that will make the light meter blissfully happy with the Ag-O battery. He just puts a small Schottky Barrier Diode in a forward biased orientation (he will know what that means) in series in one of the wires coming from the battery compartment and going to the light meter circuit. Then you just keep putting an Ag-O battery with O-ring in the battery compartment and the light meter is happy.
A more satisfying way technically with no modification to your camera is the use of a Silver-Oxide (Ag-O) battery such as the Type 357 or S-76 held in a CRIS Camera Type MR-9 adapter.
www.criscam.com/
The MR-9 is sort of a metal shell of an old PX-625 battery but with a Schottky Barrier Diode installed in it also which drops the voltage from the Silver-Oxide battery from its normal 1.55 VDC down to the 1.35 VDC that the light meter wants to see and operate from. You put the 357 into the MR-9, put the MR-9 assembly into the bottom of the camera, and the light meter thinks there is an old PX-625 Mercury battery in the camera, and it works just like it did back in the 1970s. However, there is one problem with the MR-9 that people have offered. No, not any complaint about the way that it works; just the cost or price of the MR-9. Usually it will be about $35 to $40 USD. Still, the convenience of restoring the operation of the meter back to original function with no modification to the camera, and the long life of the Silver-Oxide battery, and the very stable voltage discharge curve over the life of the battery (just like the original Mercury battery) which means that the calibration of the light meter remains the same, really are things that many people find to be worth the price of the MR-9. And then there is the amount that your camera guy may charge to make this modification for you to be compared also. It is something that you might consider and decide for yourself.
Enjoy;
Ralph
Latte Land, Washington