You're right about the fitting option.
Unfortunately not wanting to spend a ton of money does not mix well with golf clubs.
The 714's were a great club in their day but you really can't compare that to any of the newer clubs, and you need to put a lot of focus on the shafts. With the new line coming out soon, you can probably score a deal on the current line. I know it's difficult, but you need to try them out and find what fits your swing and desired ball flight. Control first, ball flight second, and distance last.

I'd think you'd be looking at T100/T150 or maybe the T200. New model release is upcoming

The direct inheritor is the T100 series The line has been expanded to sneak in a player’s distance iron, the T150 (2019/2021 version is the T100s). The AP3 became the T200, soon to be the T250.

The T100s/T150 are a little lower loft with the same bounce as the T100. Both are forged but have had other changes in COG and tungsten weighting that have improved distance and forgiveness. Finding a club version and a shaft that is optimized in LH won’t be easy. Selling your current set, and getting fit for a current new set won’t be much different than buying a used set and paying to get reshafted.