Getting back to the OP, I honestly believe that you are bound to find more ‘distinctive’ wines with other varieties at that price point, especially domestically.
This is not meant to turn into a ‘pissing match’ at all - I just find, especially below $60-70, that you will find incredibly interesting and again ‘distinctive’ wines.
Or . . . Perhaps look for cabs outside of Napa and Sonoma these days . . .
Yeah it’s not wonderful. Bottle Barn here in Santa Rosa periodically gets in Yalumba’s Cigar and Menzies and prices them well. Wine.com has been reliable for Leeuwin Art Series Cab and Penley cabs. A bottle of 2012 Cape Mentelle Wilyabrup went for $24 on WineBid last week. I don’t generally seek them out, rather jumping when I see them.
I have a few Beta’s but haven’t opened them yet so I don’t know that reference point.
When we have parties at our house our usual “house Cab” is Charles Krug - the bottles of the regular Napa Valley Cab can be had in the mid $30’s with pretty good distribution and everyone always likes it.
In a more classic style, you can try Calluna which is in Sonoma/Chalk Hill. Their estate Cab is $75, but if you join their club I think it’s 20% off or something so well below $70.
If you want something a bit more modern but still not over the top on BD I would assume you could find some Jean Edward’s wine in that price range (usually $90 bottle)
If you want something bigger- Caterwaul Wines are made by TRB and should cost $60-$65/bottle
Lastly - Elyse has their general Napa Valley blend which I think was around $60 for the 2019 bottle and its a quality blend from a few AVA’s made by Russell Bevan and if you join their club its a 20% discount and at that point a steal. You can also find it online and in some local stores.
Thanks to Larry Schaffer for the nod to me about Santa Cruz Mountain Cabernets. Unfortunately there are not many of them, $50 would be a low starting point for price and they usually need really extended bottle age to show at their best. Ridge Estate is priced at about half their famous Monte Bello and drinks well young. Santa Cruz Mountain Vineyard ‘Lucchese’ is another good bet.
I agree with the reccos for Louis Martini, especially the Napa bottling. A lot of the other reccos are for wines closer to $100 than $50 and also, IMO, wines that need significant bottle age.
Nobody has mentioned Argentina. Remove the Malbec mindset and look for producers like Trapiche (the single vineyard terroir wines, not the entry level), Catena Zapata, Susana Balbo, Norton Perdriel… you can make a long list and try a lot of wines, hopefully with some bottle age, within the budget.
Try some Bordeaux! I saw a bottle for around $16 near tge checkout stand at Discovery wines. Theyonly sell organic wines so I decided in the name of science to buy it and it was a solid bottle. Check out the selection at Astor. As others have said here Bordeaux is the best red value in the wine world and its fun to explore sub regions, producers, blends, vintages etc
I feel like OP should just accept that Cabernet Sauvignon likely doesn’t match his taste preference, and that’s totally fine! So many great wines of the world out there for a lot less money.
Now, If the goal is to find a cab that works…because a spouse loves it, or whatever the case is…I’d suggest trying something stylistically very different. Corison comes to mind, but it’s nearly double the price (but worth it). Bordeaux is probabl the logical place to look and Meyney is a good place to start to meet the budget requirement. Find some bottles with 6+ years of age for a better experience with Bordeaux.
I’m in the Bordeaux camp but also suggest that you check out Sandar & Hem Bates Ranch (Santa Cruz). They’ve had generous offers the past few Berserker Days.