I do not have a Firminator G3, however I do have a quick hitch and a hydraulic toplink. I'm sure you've figured out already that a quick hitch does not change a tractors toplink working length at all. A quick hitch lengthens all three points of the 3-point hitch exactly the same, therefore moving 3-point attachments several inches further away from the tractor, but not changing the angle of attack or changing toplink length any, and a hydraulic toplink has enough travel to use it without the quick hitch without running into a length issue if you get it short enough. The main thing that it does change is needing a longer PTO shaft on any PTO equipment, but that is rarely an issue for most PTO shafts have plenty of adjustment. I see what you are saying about being too long without the quick hitch, but I would not advise removing the quick hitch, it takes too much time and effort, and shouldn't make a bit of difference with your Firminator.
What you need to do is measure the length of your toplink at the average working length that you use it on your different equipment, and then make sure that you buy one of the correct length, where the range of travel length is centered close to the normal working length of your current toplink. If there is a variable there, I would prefer my toplink to be an inch too short rather than an inch too long, since I tilt a lot of my equipment towards the tractor for transport and maintenance purposes, but I rarely tilt equipment past level backwards for any reason. Being an inch or two shorter should also take care of your concern about using the toplink without the quick hitch.
Also, I'm sure you know this, but you really need 2 sets of hydraulic outlets for a hydraulic toplink, one set for the toplink, and one set to run hydraulic equipment with. IMO a quick hitch and a hydraulic toplink is must have equipment for a tractor, it's a huge time-saver, it really makes using 3-point equipment a whole lot easier and faster.
An FYI for anyone interested in getting a quick hitch, the worst thing is that 3-point standard measurements vary by manufacturer and I had to change hole sizes and spacings on some of my equipment to get it to all fit the same. A lot of manufacturers use category 3N size measurements with category 2 hole sizes, which doesn't fit any quick hitch right out of the box. 3N is category 2 width with category 3 height, a very common spacing found on a lot of 50 to 80 horsepower equipment, but found on zero quick attach hitches. There are several different work around options, I have a 3N quick hitch and it fits all of my equipment if I use bushings to adapt all of my holes to category 2. Yes, it sounds mind boggling, but a onetime purchase of bushings off of Amazon takes care of it.