My radiator was re-cored about 4000km ago with a brand new tripple core instead of the standard twin core which also tended to make it run a little hot on very hot days in town driving. With the tripple core it went away.
I then got a 12" for free and removed the mechanical fan. It ran hot again.Freeway it went also a tad too hot to my liking. Mine is a push fan also due to the limited space between engine and radiator due to radiator being a tripple core and very thick.
I put stock fan back and it is fine now. Fan only kicks in when standing in heavy traffic on very hot days.

Try with your current radiator and see what happens.Only thing is if it does'nt work you would have wasted a bit of money.