I D K if this will help-
Once the works are clean, oil the pivots. Everything that you see where a gear, lever, or arm is pinned or orbits on should be given a spot of oil. Some of the later made Kiev with grittier parts / gears can benefit from a bit of excess oil on the gear teeth themselves.
I've read of two large screws in the timing mechanism which can alter the speeds or the retarding action of the mechanism. But it's best not to touch these. Adjusting one may lead to a whole range of new timing issues. It's safe to assume that whoever made them probably put them correctly, or at least good enough for acceptable function.
I hope that you did not attempt to remove the upper curtain assembly. Putting it back is one of the most difficult things to do. I've done this thrice, and each time really took long to get the gears to synch right. One instance took three days to get the curtain reel to mesh right. The position of the upper curtain relative to the other gears is very important- miss it by one curtain slat or as little as a couple of gear teeth, the shutter timing at the faster speeds go bad.
I think, for the most part, you can get acceptable timing through tensioning. If you have the original, thicker Arsenal ribbons, 8-10 full turns on the tensioning screw should do it right. If you're using a lighter , thinner replacement material, 6-8 turns seem to be enough.
I've used the TV screen method. The camera is held lens-less, back cover off, facing a CRT or TV screen. With the Kiev, speed settings from 1/100 to 1/1250 (or 1/1000), I think, can be tested using this method. The Kiev runs at the same speed at these settings (the timing gears are disengaged) and rely on the slit size to alter exposure times. Because the shutter runs vertically, the camera should be held in vertical shooting position to observe the diagonal slat when the shutter runs.
If slit sizes appear to be 1/2, 1/4, 1/8, and 1/16 the frame gate's width at the 100, 250, 500, and 1250 settings respectively, the shutter should be exposing with in acceptable values.
This is the only testing method I've used, and I am getting correctly exposed pictures so far. Others may have a better way of testing the shutter timing.