Hi firewns,
The most beneficial way to carry out a meritorious deed is to hope that the good punna kamma of the deed help one (and all beings) attain nibbana.
For example if one is donating money he can think in the following manner. May this good deed help those that receive this donation live well and ultimately understand the dhamma (attain nibbana), and help me and all other beings understand the dhamma and attain nibbana.
The important point here is what we wish for when doing the meritorious deed. Wishing that whatever the meritorious deed to help me and all beings attain nibbana is the most beneficial.
As for thrihetuka births, one may never know if he has a thrihetuka birth (unless he knows that he has attained a magga pala). So the only way I see is to keep striving to understand the dhamma and keep doing meritorious deeds (as mentioned above).