Your situation is tricky. You will have to upgrade eventually, because support for 2.7x will stop (or already has?). So not doing the upgrade is not a solution, as with 140 current surveys I assume that you are using LS seriously.
I am always a fan of parallel installations for new major upgrades, because it saves me a lot of headaches. I can keep old surveys running until they are finished, I won't have sudden problems with existing surveys and I can thoroughly test new surveys.
But then I have a small number of people using LS actively (mainly me...

). With a big number of surveys and a big number of different survey admins such an upgrade can become very tricky. So I understand your point with not wanting to run a parallel installation, because of the big number of survey admins.
First of all, what I would do is to create a exact copy of my installation for doing the tests. Then I would do the upgrade. In my Version 2.73.1+171220 I get offered the upgrade to the latest Version 3.7.2 (180508), so Comfort Update would be an option.
Then I would do all the tests of the surveys, still working fine, etc. And I would create the Templates during this period as well.
Once everything is tested I would choose a time where you expect little survey traffic and do the comfort update. I know, with 140 ongoing surveys it is difficult to find the right time, but then there is never a time where nothing will happen. You will have to do it eventually.
Continuous surveys make it tricky. But depending on how you get people into those surveys, sometimes there are ways to guarantee that the flow is low (for some on the weekend, for some at night, etc.). Or if you send out invitations, then do it in between invitation waves. After 4-5 days when the invitations had been sent out, generally participation becomes very slow in my experience.
If you recruit on websites, just stop the recruitment process (probably javascript triggered) for a while and go for the upgrade then, etc.
Just a few ideas.