ProPhoto RGB is not a profile for printing with, not as the output profile. There are several profiles involved in a colour-controlled workflow. ProPhoto RGB, like Adobe RGB and sRGB as two other popular examples, are profiles based on synthetic colour spaces. These are good choices for encoding the contents of your digital file, and for choosing as so called "working colour spaces" inside various software apps such as Photoshop that you give the option to choose. Lightroom doesn't give you the option to choose; its internal working colour space is hardwired to something like ProPhoto RGB. (I'm glossing over some details here.)
Devices like monitors and printers need device-specific profiles. You create one for your monitor by running whatever calibration package you use. With printers it's more complicated, because printers produce work on papers, and each paper may have its own slightly or largely different way of rendering tonality and colour. So for printers, you want a profile that's specific to the printer itself (which includes its ink as a huge component) and the paper. In your case, you need a profile for the Epson 4800 with Epson Premium Glossy Photo Paper if that's the paper you're printing on. Epson themselves produce the profiles for their printers and papers. But since the 4800 is quite old, those profiles will have been produced a long time ago. If the profiles themselves were not that great at the beginning (which often was true years ago), or your specific printer has drifted away from the factory spec, or the ink formulation has changed (unlikely but not impossible), or the paper has been reformulated in a way that changes its colour & tone rendering (much more likely), then the ancient Epson 4800 PGPP profile may not deliver great results for you today.
If that's part of what's going on, then you'd either need to get a new Epson 4800 PGPP profile created, or find a very similar paper that has a profile for the Epson 4800 that happens to work better. You could try the profile for Ilford Smooth Gloss, for example, if Ilford makes a profile download for the Epson 4800. Those two papers are fairly similar. Using the Ilford profile would tell you if something is going on with the Epson PGPP profile if you switch the profile to Ilford in Lightroom and get noticeably different results with your print. If you use the Ilford profile in Lightroom and get very close -- but wrong -- results, then it tells you the problem most likely lies somewhere else. (Creating a new profile I won't address for now, since it's probably a red herring for where you're at right now.)
A sixth thought I'll add to my original list is to make sure your printer is actually laying down ink correctly. Your printer model is pretty old; if any of the ink cartridges in it are extremely old as well, they may no longer be printing properly. Also, Epson printers clog which means some of the small nozzles in the print head will get blocked and ink will not be laid down properly. This can cause big shifts in tone and more especially colour. So if you haven't run nozzle checks and such to be sure the printer is physically laying down ink properly, you should do that.