Upgrade from my Audio Research LS7 to a remote control model?

If you really are happy with what you have why take a chance with changing out your pre-amp for something different? I had a ARC SP10II and wanted a remote volume control so I just bought a passive remote control unit and put it in my tape loop. If your LS 7 doesn't have a tape loop you can put it between your amp and pre-amp. 

If you want to get an ARC unit with a remote control you must bear in mind that you will also be changing the sound. Subtle perhaps, or not, depending on your preferences and expectations. Better maybe, but only perhaps. Budget? Tubes? 

Why dont you get an ARC LS-15 or LS-16mki. Same sig sound as your LS-7 but much better performing all around.

You could just add this remote volume control and call it a day.  As @newbee said, a new preamp will likely change the sound for better or worse depending on your taste.  If you like your sound as is I’d play it safe and add a good remote volume control.  Placette is reputed to be very neutral and uses pricey Vishay resistors in its volume control so very likely will not change your sound at all.  Unless you think a new ARC would be a sound upgrade for your tastes, I’d just do the Placette.  Best of luck

http://www.placetteaudio.com/remote_control.htm

Wow!! looking at the remote volume control I cant understand why pay $1300 for this devise. I would rather have a better preamp that has better  soundstage and be more neutral than the LS7 for not much more $$ than the volume control. But what ever floats your boat.