Proper grip and shooting stance is essential with the desert eagle. I would never shoot a full lead or lead based bullet, dont want to have to replace the barrel.
It's a good thing you recognize this! I've had 3 DE's (2 .357s & a .44) and all of them needed the magazine to "float" (no pressure on the bottom of the mag) or feeding issues would result.
When it comes to lead bullets (or exposed lead base bullets) the Achilles heel of the DE is the gas system. Unlike some other gas operated guns, the DE gas system is extremely difficult to clean, if you plug it up with lead, bullet lube & powder fouling. The maker specifically says do not do that. They WON"T cover it under warranty!
I knew of one fellow, back in the 90s, who was convinced he knew better than the people who made the gun, and shot cast bullets from his .44 DE. I have no idea how many it took, but he DID turn his semi auto into a single shot.
The local gunsmith tried everything he could, couldn't get it unplugged. Sent it back to the factory. Gun came back with a new barrel assembly (the factory couldn't or wouldn't unplug it, either) and the BILL for the new barrel assembly. (and while I don't know about today, back then the cost of a new barrel assembly was over half the retail price of the gun!)
The only ammo you can count on running well in the DE is the ammo the maker recommends. They WILL run on some others, but if they don't you have no grounds for complaint.
Don't shoot BLAZER or any other brand of aluminum case ammo, either!
It makes no difference in a revolver, but in the (long) semi auto action of the DE, the difference between aluminum and brass cases can cause feed & extraction issues (like case rims being torn through), and this assumes that the aluminum case stuff is actually powerful enough to work the action.
The DE needs full power loads to run, anything less will give you issues, if it even works at all.
And forget about shooting .44 Special (with a JACKETED bullet) as anything other than a single loaded round. While I haven't personally tested this with the .44, I did try it with my .357 soon after I first got one (84).
Was kind of neat, in a surprising way. I chambered the round, and fired it, and the gun seemed to work, hammer was cocked for the next shot. However, when I "fired" the next round, all I got was a click. When I opened the gun by hand, the fired case came out. .38 Special was enough to push the slide back enough to cock the hammer, but not enough to eject the fired case, and it simply fed the fired case back into the chamber when it closed. I'm sure the .44 Special would do about the same thing.
Since you're not handloading for the DE, I'll skip details and tricks about that, for now.
Enjoy!!