Not going to happen. The split and rivalry were by design , Hitler and his cronies believed that competition was the way to promote excellence ( and ensure no one had an uncontested power base ). To make them work better together means ditching a key part of their ideology.
Right, this far.
The SS were the parties guardians and so were always going to get better treatment than the Heer which would cause resentment in virtually any scenario.
The first part of this is wrong. We know for a fact the
Waffen-SS (not to be confused with other parts of the SS empire) did
not "always" get better equipment, because in the beginning they very simply did not, exactly because they were a party militia and not a professional army.
Later on, once the Heer started disappointing Hitler, that changed, and yes, the Waffen-SS began receiving better equipment.
Yet the second part of your statement is entirely correct, in that even in 1939-1941, when the Waffen-SS were being armed with Austrian and Czech second-rate arms, the generals
resented them anyway; not because of the armaments, but because of
the men. Every man who was in the Waffen-SS uniform wasn't wearing a Wehrmacht uniform, and this annoyed the generals no end. It is also the reason why, after the first few divisions, the Waffen-SS resorted to recruiting abroad.