I do not intend to say that you need to invest any money into getting this fixed. The RIP that you have (Onyx Postershop 10.1) drives the printer that you have (L25500) just fine, so there should be no need to upgrade the RIP to ProductionHouse.
The L25500 has an i1 measurement device on-board, which Postershop (Media Manager to be specific) can use to re-linearize the media, so there should be no definite need to purchase another measurement device to perform the linearization. In other words, you don't necessarily need to invest anything aside from some sweat to get this taken care of, if you choose to.
I would start by taking photographs of the two prints that you mentioned earlier in this thread, and posting them here for review (one with color management turned off, and the other with CM enabled). Post them and we'll go from there to troubleshoot from that point.
Edit, please print and post images of this file (attached) instead of the other one, as it includes CMYK and RGB solid ink densities. It is also really important to keep in mind that outdoor durable printers like the HP Latex machines are CMYK devices, and there will always be finite color gamuts that they are capable of producing. These gamuts are affected by many variables, including media and ink load, etc. Some color ranges, such as electric greens and vibrant oranges are always going to be out-of-gamut for any digital printer, and are thus impossible to produce in print.
Paul