I Tried the Hero System, 5th Edition
I made a noble stab years ago at trying to convert Rifts to the Hero System, 5th Edition. Like any generic game, it meets your requirements: (relatively) quick conversion of source material (once active points are established), a better skill system (which is almost any skill system... or even no skill system at all), and an experience system without levels. It can blend magic, psionics, and technology just fine.
I didn't play it. There were... problems, and you're likely to encounter them during any attempt to convert Rifts to another system. Mega-damage wasn't one of them, though--early on, I chose to dispense with that as trying to simulate it was too much of a headache for too little reward. It didn't matter that a weapon used gunpowder to launch projectiles or fired red lasers or spat out bolts of mystic force. The S.D.C./M.D.C. divide was breached, and I didn't care--the goal was to see if characters could be evened out.
They can't. While Hero System, 5th Edition did a fine job of allowing the characters presented in Rifts to exist pretty much as printed, that didn't mean the characters ended up with the same amount of points. In Rifts one player-character can be a illiterate, penniless hobo (with candy!) and the other player-characters can be Professor Challenger, Professor X, Thanos, and Eternity, and unless you establish a vision for your campaign first that forces all the PCs to the same power level (I didn't--it was a thought experiment), there's simply no way to balance the characters.
Were I to attempt it again, I'd do exactly that: I'd determine the campaign first then work on conversions of the material necessary for that campaign, limiting myself to the things I wanted to see rather than the things that are there. I'd tier the classes, pick the ones that worked, and balance them that way, deviating from the source material to allow characters to actually fill niches.
Characters in Rifts are deliberately unbalanced. Some characters are supposed to be better than others. A grunt is worse than a commando. Any system that doesn't allow for that won't feel like Rifts anymore, but maybe that's exactly what you want.
I'm a GURPS and Hero fan, and I wouldn't think of converting Rifts to GURPS, 4th Edition, whose power creation rules are too fiddly even for a gearhead like me. GURPS, 3rd Edition, with its myriad sourcebooks, is more palatable, but converting Rifts vehicles to GURPS Vehicles is a Sisyphian task, and vehicles matter in Rifts. Hero, 5th Edition's vehicles, while imperfect, don't require calculus to create.