If you google 'delta elite case support' or the like, you should find a number of discussions on the topic, along with comparative photos showing the issue therewith. Not sure what aftermarket barrels might be available to improve the situation.
While you specifically said you didn't care for EAA or the guns it offers, you may still want to consider the Tanfoglio Witness Hunter--EAA doesn't make any guns as far as I know, and Tanfoglio makes a number of extraordinary ones, IMO. The reason I still suggest a look at the Hunter is: all steel, single action only, double stack, 6" fully supported barrel and dead nuts accuracy. In spite of being a double stack, it doesn't feel the least bit fat to me, and I have average/medium hands with relatively short fingers. This is about as much a 1911 design as you can get and not be a 1911. It is beautifully made and finished, but of course 'unique' in terms of sights, trigger and of course the way the slide rides inside the frame, not on the outside.
If it's still thanks but no thanks to the Witness Hunter and has just gots to be a more 'true' 1911, then only based on comments of those who hang around the 10mm crowd, it's been the Fusion line that I've heard the most of, all positive. What I think is real nice there is that you can get pretty much anything you want at what I think are semi-custom prices. I have an upper limit as to what I think
any handgun is worth, and many custom 1911s are way beyond that. Fusion seems to retain some sanity while offering some beautiful guns--all of them in 10mm, or just about. That would be my first choice, but I don't own one and never fired one.
As for not reloading, 10mm ammo, when available at all, is comparable in price to any other full-bore auto pistol ammo: $0.75 a round is possible with Underwood, and even lower prices can be found on ammo that doesn't exist.
I don't see 38 Super being any more available or even remotely less expensive than 10--I wouldn't plan on price being a differentiator here. I will say that 38 Super in a longslide 1911 is fun, but 10 is funner.
Now, you didn't mention any particular purpose to which you'd put the gun, so that might be useful to folks. If you were considering a Delta I assume this isn't a carry gun, but I'm among those who find 10mm to be just the most perfect and versatile auto pistol cartridge devised, and I carry it every day--just not in a 1911. I would truly enjoy a CCO format 1911 in 10 for that purpose--if I didn't already have a Glock 29 to fill that role. Again, Fusion comes to the rescue with gorgeous options in the smaller 1911s.
Go 10--you'll be glad you did. When you do get into hand loading, the options for that cartridge abound.