The FSS has a different designed sear. That may be why Apex said it needs the 1/8 inch spring to supply more pressure. Apex has three sears for the M&Ps. The FSS is used in conjunction with Apex's trigger and the same sear is used in the 45, 40 and 9mm, but not in the Shield as Apex doesn't have the FSS kit for the Shield.
Then per Apex:
"The only difference between the DCAEK kits for the Standard M&P 40, 9mm & Shield kits compared to the M&P 45 kits is the sear itself, except that the Shield kits differ only in that they use a smaller slave pin for installing the trigger spring. The Competition kits use the exact same parts, except for lower pressure springs. Since the 45 has a shorter trigger bar in relation to the engagement point of the sear, which means we had to move the sear lobe forward by X amount on the 45 sear to make it work in the 45 frame every time. In some cases the standard sear can be used in the 45 and the same is true the other way around, but to keep things consistent when it came to trigger pull weights and over travel distances, we created two different sears. Using a 45 sear in a standard M&P will yield a longer over travel, by a slight amount and decrease the pre-travel an equal amount. In our years of professional training and shooting, we found that by eliminating over travel to less than .030 of an inch, we achieve better accuracy across the board, so the decrease in over travel was most important with the production of the 45 sear."
Since you can't find the newer 1/8 inch sear block/housing, why not give the stock 1/16 spring a try, it can't hurt anything. I would think the issue is needing higher pressure on the sear, than the 1/16 stock spring can supply. However if you put a very short spacer under the 1/16 inch spring, to raise the spring no more than 1/16 inch, that would increase the spring pressure greatly. It may need as little as 1/32 inch spacer to work properly and who knows it could work without any spacer. The sear spring's only purpose is to raise the rear of the sear, that is all it does. Because the FSS moves the trigger break point forward, the issue should be keeping the sear raised higher, to catch and hold the striker. The FSS sear is designed differently and the top of the sear, where it catches the striker, may have less height than the other sears and thus the height that the rear must be raised could be greater. I don't know as I do not have a FSS sear, but I do have the stock sear and the Apex DCAEK sear.
A sear pressure test you can do is remove the slide on your current gun and test pushing down on the sear with your finger, getting a feel how much pressure is needed to get the sear to start to move. Then when you install the FSS kit, test the sear pressure the same way. Try to get a similar pressure by changing what you need to use as a spacer under the 1/16 inch spring.
You can't do any damage to the kit or gun, other than it may not fire properly (FTF), but this should in no way damage the gun or kit. After install test it by dry firing. If you can get it to dry fire properly (watch the Apex video for adjusting the timing on the sear loop), then load the chamber with one round, insert an empty mag and test fire. If all works properly, load one round in the chamber, and one round in the mag. Test fire two shots. If this works keep adding more rounds in the mag, and test fire two shots. The more rounds that are in the mag will cause more upwards pressure on the rear of the slide, and per the Apex video, raising the slide can cause the sear to release the striker sooner. If all tests OK, then you should be good until you can find and install the 1/8 inch sear housing.
Or you can wait until you can get the new sear housing.
Bob