My 1991 CBR1000F (California) had carbon buildup on an exhaust valve. I pulled the head, cleaned the valve and seat, checked all the valves for leakage, and reinstalled the head. I'm now having trouble setting the timing. When I set the sprockets with the IN and EX marks parallel with each other and with the top of the head, the timing mark is at the "F" instead of the "T":

Timing mark at F instead of T

When I move each sprocket one tooth in the chain and align the marks properly again, the timing mark is past the "T" (the shorter timing mark lines up with the "T"):

Timing mark past T

The engine had been cranked several times to get everything to seat properly. I've rotated the engine and rechecked this several times, and the results are always the same (at least it's consistent!). What can I do to get the timing set properly? I'm trying to use this as a teaching tool for my son who has started working on his ASE certifications to one day become a master mechanic, but I'm not doing very well!

 

You didn't provide a picture of the sprockets aligned with EX-IN at the cam cover interface. Make sure the UP stamped into the 2 sprockets are facing to the left of the motorcycle and that they are at the top (i.e. UP) when aligning the EX-IN scribes at the cam cover interface.
Always turn the engine in the direction of normal operation when aligning the sprockets. If you go past TDC, turn the engine back some way and then approach TDC again in the normal direction of operation (anti-clockwise looking at your pictures).
That said, how does your cam-chain look? The angular position of the sprockets relative to one another is governed by a stack up of tolerances in the crankcase, cylinder block and head dimensions, plus the variability of the gaskets' thicknesses compounded by the amount of squish the gaskets get due to the torque tightening of the cylinder head nuts, as well as the amount of stretch in the chain. This last item is probably the mots variable of all; a new chain and a worn chain will locate the cam sprockets relative to the crank pinion differently. It is not an exact measure as you have discovered. If the chain is new, I would expect to see a slightly better alignment that you have. If the chain is part worn, you might expect to see the crank location go past TDC (your second picture). The first picture shows a larger misalignment and it is prior to TDC which is difficult to rationalise. In these cases, choose the alignment that gives you the closest to the intended one.
I had a CBX1000 (the 6 cylinder beauty) which had about as much misalignment as you are seeing, even with a brand new chain.

 

I used a steel scale to make sure the IN and EX were aligned with the top of the head:


IN aligned with the head

EX aligned with the head

I've rebuilt several car engines, and I've definitely seen the chain stretch as miles accumulate. This is the first bike engine I've done any significant work on. The bike has only 10k miles, so I wouldn't expect the chain to have stretched much. I set up a fixture on top of the head and measured to the IN and EX marks as well as directly opposite those marks on each sprocket. The measurements were all within a few thousandths, so the chain stretch can't be much. The new head gasket is from Honda, not aftermarket, so the thickness should be correct. The head bolts were tightened in a staggered fashion up to 33 ftlb. The guides look good. The tensioner moves a lot when pulling a sprocket off a cam, but when putting the sprocket back on, the tensioner doesn't move much before tensioning the chain, also leading me to believe the chain isn't stretched.

I did those checks and measurements because, with the low miles, the cam position error is surprising and doesn't make sense to me. Thank you andy_williams for your thoughts and ideas. The inaccuracy may indeed be just due to wear. The final thing I'm going to try is pulling the cams and checking the torque on the head nuts.

If what I have is the best I'm going to get (without going to adjustable sprockets), I might do something "creative". I compared the 48 state cams to the CA cams, and then how the properly aligned 48 state cams compared to the CA cams that are out either before (about 2/3 tooth) or after (about 1/3 tooth) the index mark. The CA exhaust cam looks better at +1/3 tooth, while the CA intake cam looks better at the -2/3 tooth. I think I'll try that and see how the bike runs. Since I don't live in CA, if I want to put some money in the bike in the future, I'll get 48 state cams and rejet the carbs (I've already removed all of the CA emissions junk).