dont know why you havnt considered it in the current climate, probably not interested but its you're choice. If you want to rush off to the airlines the logical path is through instructing.
I think you will find the airlines traditionally prefer charter guys. Flight Instructors without any real world experience have very distorted views of commercial aviation and once become ingrained in their ways are very hard to convert to a charter pilot.
Multi in a PA-44 it looks the same as PA-31 on paper to an airline.
There is a big difference and they know it!
Remember what the airlines are looking for too, they dont care if you can get a heavy Baron into an ag strip on one engine during the middle of the wet season.
This is called experience and is something that they are looking for. Wet season flying is a different kettle of fish to circuits in a 152 or ME instructing in capital cities.
They want to see that you can work in a multi-crew environment conforming to their SOP's and that you know the regs like you wrote them. Whats a better environment to learn that in?
You will have a very good grasp of the regs in charter as you need to know the rules you sometimes bend!
When you are required to fly multi crew you will adapt just as everybody has that went before you. It's not very hard, you just need to tell the guy next to you what you plan to do and ask him for suggestions. The rest is standard calls and idiot proof (much easier than single pilot IFR)
Anyway, like I said, your call but I know which path I and all of my colleagues chose and then there are those who chose... the former.
Of course, thats because all your colleagues are instructors! Just as mine are charter guys! I bet you all talk about charter like you wrote the book on it too!
Things to consider:
I'm not in an airline but that's my choice I'm where I want to be however all of my previous colleagues had instructing backgrounds and First job to airline was between 3-5 years.
Traditionally charter is much quicker to the Airlines if that is what you are chasing. As an instructor you need to become a grade 1 to get any multi engine work, and that can take 3 years in itself. Then there are the 50 hours command for your META standing in your way which is a huge hurdle in itself
You can be a slacker and stay in the City.
You can hang onto the dream that this COULD be a 9-5 job
Despite what you will think at the time, you will get treated the BEST out of the whole industry as an instructor.
Instructors are and always have been treated as the bottom rung in aviation. Most of the time in charter your first job will be full time and paid accordingly. Most operators pay the AFAP award. Becoming an Instructor you need to scab, find students, work as a contractor, hang around the flying school helping out 7 days a week for free so they will toss you some crumbs occasionally. It is a very demoralizing existence starting out and can take over a year to get the hours to become a senior 3! (has been a bi easier in the last couple of years but prior to that it was nigh on impossible)
And yes I have an instructing background as well however I was a charter pilot first in the tropics so I can comment after being on both sides of the fence.
It's a slippery pole to climb and you need to work out the best way for you.