The situation you described below is proof that the hairspring dog leg is not following the curve of the regulation loop. But it is usually the extreme ends (full fast or full slow) when the clock is out of the case, that is not normal operation. When the clock is in the case fully assembled the regulation sweep is shortened.
But, you have not answered the question of how fast the clock is running. So if it's only minutes a day off then , hey it's an alarm clock, not a astronomical time keeper.
If your a beginner I would not recommend hairspring work till you get more experience with more disposable clocks.
If it's much faster per the day then you may have to restore the hairspring.
The rule for bending is for "out of round", 90 degrees before the error result is seen. So if a coil is obviously wide or narrow (touching another) then go 90 degrees before that and bend there.
The rule for bending "out of flat" is 180 before.
For the bending of out of round, the bend happens where you grip the spring with the tweezers. You can use any object to bump when the spot you desire to bend is held next to tweezer tips. So basically grab where you want it bent and use your finger tip to flex the result.
For bending out of flat you use 2 tweezers. Grab 180 degrees before the result with one tweezer and next to that with other tweezer roll the one tweezer so that it bends a twist. This twist action is harder to do than out of round but with enough practice you can get errant coils to lay flat.
There are only two other hairspring modification tricks. One is the untangle of a cross over loop. The cross over loop happens when an outer coil works it way by accident in between inner coils.
This can be easily solved by grabbing terminal end of hs, stretch moderately and orbit in figure 8. Sometimes it works -sometimes not. Sometimes you have to work the errant coil outward with needle working the coil to outer coils. Then try the 8.
The next trick is for coned hairspring coil. A cone happens by accident when a hairspring is stretched and forms a cone. This is fixed by stretching the hairspring cone in opposite cone. Test stretch and take small measures first for results.
Beat:
The hairspring collet that connects to the balance wheel arbor is friction fit to the arbor. The collet has a slit that you can insert a small watchmaker flat blade screwdriver into.
If the hairspring has descent form, coils are in-line from side view (called true in the flat) and coils are not touching and the coil is evenly spaced (called true in the round) and the dog leg (bend that conforms to regulator and is staked at the terminal) is reasonable, then you may need to work on the beat.
The beat of the balance wheel has to do with the balance working equal distances on both entrance and exit. Look and see the small pin that is on the side of the balance wheel. This pin interacts with the palette fork.
If you can, look at movement from side view and examine the rotation of the pin while the balance turns back and forth. If you draw a straight line between the lever arbor and the balance wheel, you should see the pin appear in equal amounts on both sides of that line.
To be in beat the pin pushes the lever in equal amounts for the entrance palette and exist palette. If you find that the pin favors one side you can change this in the following way:
Insert a flat blade screw driver into the hairspring collet. You may have to rotate it with a finger to an accessible position. Insert the blade holding with one hand, with other hand/finger CAREFULLY, SLOWLY rotate the balance forcing the friction fitted collet of the hairspring to give and allow the balance to turn. Rotate till the pin is in a better position.
The evidence of a good beat is evenly spaced "tick-tock-tick-tock". Unevenly spaced "tick-tock...... tick-tock......tick-tock is evidence of not being in beat.
Though this expression may seem crude it points out that there is a different sound between entrance palette(tick) and exit palette(tock). So you understand.
After you have established the clock to be in beat, check and see what the results are. Beat however is not really related to time keeping but more to keeping movement working.
The other thing left is to re-pin the hairspring at the terminal. If you are lucky you will have extra length left over after the termination. You will most likely see a taper pin inserted in the termination block.
So, you want to terminate at a longer point. Depending on how much extra you have left you can experiment at about 1/8th inch intervals.
But understand, when you re-pin the hairspring at the terminal, making the effective area of the hairspring longer, you will have to re-establish the beat. You can get away with some re-pinning without losing the beat too much, but, the more you add the farther the pin moves out of the alignment for equal "tick-tock".
In the probability matrix of cause and effect, I would suspect out of round, out of flat and maybe touching coils.
RJ
Well the Balance appears to be rotating somewhere between 270 and 360 deg. One thing I noticed though is that when the regulator is pushed all the way to the slow end, the hairspring is in the center of the regulator loop, but as I push it toward the fast end it rests on the outer edge of the Regulator loop. Also the inner edge of the regulator loop touches the main body of the hairspring when it is toward the fast end.