I write and throw with my right hand but have a left dominant eye so have always shot rifles and shotguns left handed. (I've also shot competitively with handguns -NRA PPC- and shoot as well left handed as right handed..).
I prefer the Marlin lever-actions. I like the Winchester M94 and others, but due to scope mounting, I've preferred the Marlins. I've got a Glenfield(Marlin) M30 in .30/30, a M336C in .35Rem, an 1895 in .45/70, and a new .338MX in .338MarlinExpress. The latter is my current "darling". An aquaintance I was recently hunting with remarked as how he could tell I shot it left-handed as I had a butt-cuff for the ammo on the left side of the stock, and the hammer extension switched to the left side. I also have a Winchester M94 "Legacy" in .45Colt. Very nice rifle. Not crazy about the range limitation of the cartridge, but with a "warm" handload with a Hornady 250gr XTP has hurt the feelings of some bolt-action/scope sighted rifle shooters. It will approach MOA at 100yds with a reciever sight !
I also have a Thompson-Contender in 7-30Waters that I'm rather fond of. Being a single shot and operated by the squezing of the trigger guard to semi-cock and open the action, it too is an "ambidextrous" action.
I too, have 3 Remington Mod-7's. The light weight and balance allows easy retention of shouldering with the left hand and operating the bolt with the right. I'm sure it looks funny, but it works for me. .223; .260Rem; 7mm08. One of the latter two may eventually get retired or traded as they "overlap" in function. (Deer, pigs, elk)
I have a Savage M110LH in .30/06, but it's not a favorite rifle. It's not particularily accurate. And, it dosen't care for ammo loaded above factory pressures as the action lacks the "camming action" upon opening/extraction of the mainstream actions such a Rem M700's, Win M70's, or the 98 Mausers, ect.... It even has sticky extraction with "warm" factory loads.... It's getting sold, soon.
I also have had a Remington M760 that I was fond of, but lost interest in it due to the poor ergonomics of the forward slide and that it "rattled" badly, several times scaring game as I "manuvered" the rifle into firing position while deer hunting from blinds or deer stands. The rifle was in .35Rem and was used for hunting in "wooded" areas. It's role was later taken by a Marlin M336 in .35Rem. Not quite as accurate, but a superior machine for it's purpose....