I have a mix of factory and semi-Custom/full custom left handed rifles. They are out there, and it may take a while to find one that fits your desires, but they do show up from time to time.
While LH Rem 700 are common, the short action ones seldom show up for sale, and do not last long. But as a donor, the Rem 700 has the largest after market share for options to customize.
The Brownings, A Bolt and X bolt, are both good rifles and shoot better than most people give them credit for. As mentioned above, the X Bolt All Weather is a great rifle, and can be found in short, short mag, and long action versions. I have a 6.5 CM, a 270 WSM, and a 308 Win that is being rebarreled to the 25 CM. This rifle has one of my all time favourite stock configurations. There were two versions, the latter having a slimmer barrel profile and a muzzle brake. The newer X Bolt 2 is not available in LH (or at least not yet). I really wish they had made the Mountain Pro in LH!
As you stated, the LH Tikkas only come in a long action, with a block in the magazine. And they have a great reputation for accuracy. I just prefer the fit and finish of the Sakos, but this is just my preference. And I like the various action lengths and nicer design (again, my opinion) of the Sako Model 85 DM. I like the double stack vs the Tikkas single stack magazine. I do not find the newer Sako Model 90 worth the jump in price over the Model 85...and I would recommend you watch for a LH Model 85 in a short action. Great rifles that provide a lot of features compared to the price of a custom. Another rifle that I also really like the factory stock configurations (wood and synthetic). My most expensive rifle is a LH short action Model 85 Finnlight II that I had rebarreled with a carbon fibre barrel. Got what I wanted in the end, because no one offered exactly what I wanted, but I had to budget for it. To me, it was worth it. I have a fairly lightweight rifle that will cover about 90% of the hunting I do. And while it doesn't have a pretty wood stock that I can admire, it has a very utilitarian synthetic stock that will survive the mountains and deep, dark timber, and bad weather it may be subjected to. (I do have a couple of other rifles with beautiful wood that I can admire wen I need to!)
One in great condition should run about $2200...and yes, they did offer a few LH in the Carbonlite, but very hard to find and were about a $1000+ more (used) if you did.
The Winchester Model 70 was available in a LH short action, including the WSMs. Not many out there, but they do pop up every now and then, Again, they do not last long. I just wish that the FN version had been offered in LH when they were making them for a few years. Their fit and finish were very nice , and just about every one came with very nice wood. The newer versions were being barreled by Bergara if memory serves.
Ruger made LH rifles over their various models and configurations over the years, and are rugged, reliable rifles. And I have not owned one that wouldn't shoot at least acceptably well. I have used the Model 77 Mk II for my DG builds. While I didn't really need the claw extraction for these rifles, as I have never had an issue with a push feed action, the donors were the only LH ones I could find at the time. But it doesn't hurt that they have it. I wish that Ruger would have offered their RSIs in LH! (Although the No.1 RSI isn't sensitive to a shooter's handedness!) Beautiful little carbines! My custom LH Ruger in 376 Steyr actually is in a LH Wenig laminated mannlicher stock, and is a joy to own, shoot, carry, and hunt with! Not as light as the RSI, but who wants a DG rifle too light! LOL
Savage offered several variants in LH, and they shot well. (Just not my preference, but again only my opinion...life's too short to own an ugly gun! LOL)
I did not play with Antler or Fierce when they were made by Antler, but cannot complain about my new LH Fierce Carbon Rogue in 7MM PRC. I did look at the Christensens and almost went with one, but did not like the stock's thin wrist, and the wide range of accuracy issues I was reading about, and hearing about from my gunsmith. I got everything I was looking for, for less than a custom build.
As for Bergara, I would be tempted to try one of the newer versions with a more classic stock design, as they have a pretty good reputation, but have not even seen one in a LGS to even handle one as yet.
Steyr makes some great rifles and I have two LH Steyr Mannlicher FS rifles, but they are very rare! And I have the only two I have ever seen...although the 270 is up for sale now that I found the Special Edition in 6.5x55.
Sauer also made some nice LH rifles, and who knows...maybe one day...
Blaser also makes LH rifles...and they definitely are not budget friendly. But who knows...IF I sold a few of my other rifles, I could afford one...but which ones? Maybe one day...when I actually start to downsize...
If you cannot find exactly what you are looking for in a factory rifle, your only other option is to go the semi-custom or full custom route. The semi-custom can be as simple as a rebarrel or rebore job. (Be prepared to add $1000 to your cost to rebarrel with a quality barrel, but there are some great options to choose from, and then you can get the proper twist for the cartridge and bullets you intend to use.) The full custom can get as expensive as your wallet allows. Only you can determine what works for you. Just remember, it will be your build, so make sure you plan accordingly, as you want the end product to fill your needs and desires. And plan accordingly for the time to get it built.
And you will never recoup your investment in a resale, unless you find the right buyer that wants the exact same thing as you (which is rare!), willing to pay your asking price.
The recoup in your investment is the satisfaction you get with the end product that fits your needs and desires, and adds to the richness of the adventures of hunting, shooting and owning that firearm in the years to come, and the memories it will bring you. = Priceless!
Best of luck in your quest!