To quote Hartwig:
Oxidative addition to more electron-rich metal centres tends to be more favourable than oxidative addition at metal poor centres 
This is generally a thermodynamic issue, and can be rationalised quite easily if one considers that the change in electron density at the metal centre during the oxidative addition process (note, theres a difference between formal oxidation state and the 'actual' electronics about the metal centre).
As you point out, most catalysts systems used are either Pd0 to begin with, or generate Pd0 via a Pd2 pre catalyst (the palladium needs to be in its 0 oxidation state for oxidative addition to occur, usually, though 2 -> 4 is also possible in certain circumstances).
Your confusion seems to have came from the actual nature of the active catalyst, although you'll always end up with Pd0 , the metal centre has ligands attached, and these ligands are able to tune various properties at the metal centre.
The issue with trying to optimise a reaction ( as you seem to be doing) is that there is an almost infinite number of combinations of catalyst + ligand that you could consider, and indeed chemical companies such as Sigma-Aldrich even sell screening kits which provide many of the most common.
My honest advice in your situation would be to have a thorough search of the literature and try a few combinations of ligand + catalyst that you have available in your lab. Doing the optimisation rationally can be extremely interesting (doing it properly requires changing catalysts, ligands, solvents, temperatures, additives etc and is all time consuming, though often done in industry during optimisation before scale-up), but is of little use synthetically if you simply need to drag material through.
: Hartwig, J. Organotransition Metal Chemistry- From Bonding to Catalysis; University Science Books:Herndon , 2010