jlp, yes, you can remove the factory tee and put in a brass one.
If you have the hoses apart. I would recommend taking some compressed air (regulate it down to around 50 psi until you know things are clear) and use that to blow back and forth through the heater cores. It may be that you simply have a blockage in the pipe and by using some compressed air, you can push the blockage out.
I have also found that using a small amount of water and "shooting" it down the pipe is a good way to dislodge a blockage. This is called "water hammer". Normally this is a bad thing if you work around piping systems. But, under certain circumstances, it can be beneficial.
Once you can get a decent stream of air through the core, you can then turn up the pressure and try to get some serious air flow to help blast the remaining crud out of the system.