Print a profiling target but with your normal color management turned on. Look at the red patches, pick the one you like the best, then make sure your reds have the same RGB's. Or just make a lot of prints until you get your red ignoring everything else, then make some masks and control layers to balance out the rest of the print. Sounds like you've already done that.
The Epson 78xx and 98xx can do a pretty decent red. But if you've got a critical color then you have to hit egg-zackley the right density on the print, no printing down or up allowed. Of course every color print creating system has the same problem.