Diagnose your situation.
1. Record the velocity of each shot along with the position of each shot on the target.
2. Using a ballistic computer check that the vertical stringing correlates with the variation in muzzle velocity. You don't want to chase a loose scope
by adjusting loads.
3. How good is your velocity consistancy? Calculate it in terms of standard deviation and extreme spread.
4. Vertical stringing increases with the SQUARE of the distance for a given velocity variation. What range are you shooting at?
5. Are your expectations for vertical stringing realistic?
for any bullet without atmospheric drag at 1000 fps the time of flight and drop are:
yards sec feet
100 0.3 1.44
200 0.6 5.76
300 0.9 12.96
400 1.2 23.04
500 1.5 36.00
600 1.8 51.84
Real bullets of course slow down with distance so the time of flight and drops are always greater than the chart above. Very high BC subsonics like the 50 Whisper with Barnes solids are close to the above chart. Pistol cartridge subsonics are much worse. Calcuate the expected drops for the bullets you're using.
A 1% change in velocity gives close to a 1% change in the total drop.
For 1000 fps a 1% change is 10 feet/second.
1% variation high BC ammo will string about 0.17 inch at 100 yards. (one hole groups). It will string a lttle over 4.3 inches at 600 yards. That's still good for hunting with careful range measurement.
You shouild be able to get that velocity spread with careful handloads. You should expect some effect in that order from a cold to warm barrel. With careful powder selection that can be improved a little. It's very unlikely you can achieve 0.1% or 1 fps variation even with the best benchrest loading techiques. If you're getting greater than 20 fps variation you can probably do better.
Use a program like Quickload to check:
what is you % case fill? Around 95% is most desirable. Use a less dense powder to raise this number. Under 80% will hurt velocity consistancy.
What is the peak pressure? Around 90% of SAAMI max is ideal for safety and long gun life. Under 80% will hurt velocity consistancy. Faster powder raises this number. There are jumps and gaps in avaiable powder density and burn rate. Sometimes the only solution is to use a different cartridge.
That should not be a problem with a 300 Whisper and available bullets.
Fortunately the 300 Whisper is a high pressure cartridge. Use it as such with fast bulky powders for accuracy. That may not be best if you're trying to also cycle a semi-auto.
Do your bullets seal the bore before firing? That's desirable particularly for subsoniics to prevent blowby. Blowby can cause huge velocity variation. Losing 1 grain of propellant gas before the bullet engraves makes a lot of difference if you only have 4 grains to work with.
Are your bullets the right diameter? If the bore is slightly oversize or the bullet slightly undersize there will be blowby and velocity consistance will be bad. Too large of bullets will give high engraving force and high barrel friction which also hurts velocity consistancy.
Here's a speed video clip showing blowby from a slightly undersized subsonic bullet. Note the the smoke >before< the bullet reaches the muzzle.
http://www.kurzzeit.com/eng/startseite.htm
Is bore friction variable? Bore friction doesn't necessarily have to be low, but it must be repeatable. Velocity will be more uniform if the ratio of chamber pressure to engraving force and bore friction is high. Lubricants
will lower bore friction but they don't necessarily make it more uniform.
That requires getting the right lubricant and application.
Are you using a long barrel? Most subsonics need only 8" to 12" barrels for best accuracy. 16" may be needed - for legal reasons. Longer than that is just throwing away accuracy. Again, the ratio of chamber pressure to bore friction needs to be high or the variabilty of the bore friction from shot to shot can ruin velocity consistancy.