The problem is only partially the Senate, which despite the ultra-conservative rump included enough people who were open minded on the Italian issue that it was a goer, as evinced by all his measures passing the Senate. The problem is the plebs. A bit like dirt poor whites in the US South Roman citizenship and it's exclusivity meant much more to the lower orders than to a patrician who was going to end up on top whatever happened. In the Senate the opposition to his efforts disproportionately included New Men. His dangling the prospect of land reform had brought him an awful lot of goodwill but once his proposals for enfranchisement of the Italian came out it disappeared very quickly, not least because the Roman plebs realised that several million Italians would be joining them in the queue for the dispersed public land. Add to that land reform was killing his support in the Senate despite their gratitude for giving them back control of the law courts and it's clear his reform program was near death even before he got stabbed. So to save it you need to change it and moderate it. Either by restricting the Italians to the Latin Rights or by restricting the land reforms to "Roman" Roman citizens. If he's got enough support from the Second and Third classes in the Assemblies he can manage the Senate to an extent though a few more judicious concessions, like scaling back the grain dole on the basis that land reform would reduce the number needing it. Even at this stage the Senate tried to avoid confronting the Assemblies.
The other issue is the oath of clientship, that has to go otherwise the Republic becomes an Empire ruled by the Livii 50 years early. It's a complete non-starter and unless he disowns it and releases everyone from it the moment it comes out everything he's done will get repealed just like OTL.