For speed dominant/lower revs, don't just go by asymmetrical/symmetrical cores. Look at the core numbers/RG numbers as this will be your best indicator for what will match best.
Low RG balls tend to work well with medium-heavy oil as they will pick up on the lane the earliest. Medium RG balls will conserve a little more energy and will tend to be an even arc throughout the lane. This means you'll have a little more length but still have something smooth throughout. High RG balls are going to go long but be strong in back due to conserving the most energy.
Then, take a look at the differential. Low differential means that the mass is more towards the center of the ball. This means the ball is more "core heavy." Medium differential means that the ball will have a good combination of center mass/cover, and High differential means that the ball will be "cover heavy", or that most of the mass is in the cover.
In this case, if you need something for heavy oil, look more towards a low RG/medium to high differential ball. This will allow the ball to compensate for higher speed/lower rev rate on that type of condition. For your medium conditions, you should still look towards a lower to medium RG ball with a medium-high differential. This again will compensate. Then for dry conditions, lean more towards a medium RG/medium differential ball.
For covers, you will benefit mostly with solids or hybrids. I always throw the ball with the box surface first to get a read on how it will react. If necessary, I'll change the surface to match even better. Don't be afraid to do this.
Pearl covers, unless the surface is adjusted, may blow through the break point in the back of the lane and not read the lane properly.
Hope this helps. I know some others will probably chime in with some other info or can be more technical.
