Hmm, yeah.. So maybe the quick and easy is to just use some brownish clear on top of it all? To be honest I was leaning towards stripping, sanding, oiling and waxing, for that nice feel..You’ll find out once you start stripping it but the red is most likely a tinted or candy clear. That’s typically how Gibson / Epiphone do that color. Also, how their and Fender’s bursts are done. As others have said you might be surprised at how light the “mahogany” body is once stripped. It will probably require some help to look like your second picture. That would also be best achieved with a tinted clear coat. You can try staining or, better, dyeing it but it’s difficult to get all of the sealer out of the wood and even if you do it can take the dye unevenly.
Would this affect the weight noticeably too? It's already a bit on the neck-heavy side..