I too am right handed but left eye dominant, and over the past 38 years of hunting, I have transitioned from right handed rifles and shotguns to left hand as much as possible.
I am 6' 2' with a long back and wide shoulders, so my Length of pull (LOP) is longer than the average shooters and while it makes a difference, when hunting in cold weather with bulky clothing a regular LOP is not necessarily a handicap (and is any of your moose hunting later in the season?). On a number of rifles, I have installed after market recoil pads to add a little extra LOP.
There are several different manufacturers who make, or used to make, left handed firearms. And a used rifle may be a better purchase if you find what you are looking for at a good price. I have done this several times over the years.
Remington Model 700s were the most available in LH, and can still be found at prices comparable to what has been mentioned above. They are a push feed design that is known for its accuracy potential. Most of mine have been very accurate. Some models did come with a detachable magazine. There are also more after market options available for Rem 700s than just about any other make and model, so you can always alter one to your satisfaction.
Ruger is another maker that offered their M77 and Hawkeye rifles in LH. These too are robust rifles that offer a CRF type of action for rugged reliability. They can be a little heavier, but this can aid in holding steady on target off hand when your heartrate and breathing is at a faster pace, or buck fever has hit. I have not owned one that was not at least acceptably accurate. They also offer the American rifle in left hand for a less expensive option. These have developed a reputation for accuracy too.
Savage offers left handed rifles as well, and another pushfeed design that has developed a good reputation for accuracy.
Browning offered LH rifles, in wood, synthetic, and laminate models, in both the A Bolt and X Bolt designs. They too have detachable magazines. I have not owned a Browning that was not acceptably accurate, with most being very accurate. One of my favourite rifles is their discontinued X Bolt All Weather rifle (stainless in a pepper laminate stock), and these can be found for sale used from time to time. The Hunter is wood and blued, and also a great rifle.
Tikka has probably been the most prominent and available LH option in the recent past. Another push feed design with a detachable magazine, that has developed a good reputation for accuracy. While they offered a wooden stock, it was not as available in left hand, and not in laminate.
Sako also has LH rifles, and are of higher quality, fit and finish than the others listed here, and demand a premium price, but are good investments, as they are well known for their smooth push feed actions (floor plate or detachable magazine) and accuracy.
There are others such as Weatherby, and Winchester, which you'll have to find used, and so on. The ones mentioned above are the most common.
As mentioned watch the Equipment Exchange for left handed rifles (use search), publications such as the national firearms paper (Canadian Access To Firearms), and other online sites such as #######, where there are currently 140 left handed rifles listed for sale.
Where possible, try to handle some of these rifles to see which fits and feels best to you when you handle and shoulder it.
As for caliber and cartridge, you'll find a pretty good variety of short, and long action rifles and cartridges, including magnum offerings. For your typical moose hunt out to 200 yards, the suggestions of the 308 or 30-06 are solid choices. There are also a number of good cartridges that would work for you too, ranging from the 6.5x66/6.5 Creedmoor, 270 Win/280 Rem, 270 WSM, 7mm-08 Rem/7x57, 7mm WSM/Rem Mag/PRC, 300 WSM/Win Mag, 338 Federal, 358 Win, and 9.3x62/9.3x74. Your choice will be whether you prefer lighter/faster cartridges, or slower/heavier. And your recoil tolerance will also factor into your final decision.
As for scopes, there are many good choices out there...BUT do not cheap out on the scope! Quality glass will ensure years of good, reliable service and assist you with accurately placing your shot in the vitals for a quick, clean harvest. These older Leupold scopes such as the VX-3 are rugged and reliable, and have a lifetime warranty regardless of the owner, and are a great option. Highly recommended by me, as well as many others.
Hope this info helps!
Best of luck in your quest!
