The only way I can see to affect the chance of getting snoutling offers in the dojo vs. LC offers is to avoid leveling any class to max mastery until you are ready to max out that entire bird family.
For example, if all of your birds are below max mastery, you have about a 12% chance that once the first two slots are populated with LC offers, the third is as well. If you max out one full bird family, that chance drops to about 11%. Two bird families – 10%, three bird families – 7.5%, four bird families – 0%.
Odds of getting an LC offer actually increase if less than the full family is leveled up, worst case being if you have only one class for each family left to max out, in which case the chance of getting an LC offer are a whopping 45.5%
This is pure math, assuming that there is an equal chance of getting any of the available options at a given time, and does not factor in any special weighting that Rovio may have coded into the system.