Your 3000psi is probably 48ci (0.8 litres), on the link below a 48ci @ 3000psi with a 'gas pig' would give around 504 shots
A 1.1 litre would be 68ci. So if you still only have a 3000psi fill at the site you would get 714 shots (due to the bigger size)
If you had a 4500psi fill that would give 1071 shots
If you were to get a smaller 48ci 4500psi cylinder (These are the same volume as a normal 3000psi cylinder, but usually shorter and fatter) then you still get 504 shots with a 3000psi fill, or 756 with a 4500psi fill
http://www.scubatoys.com/paintball/paintballshots.asp
Just getting a fibre 4500psi cylinder won't give you more shots, it depends on the fills available. If you have 4500psi available at the site then getting a fibre will allow you to get the full pressure available.
If the site only gives 3000psi fills then a bigger cylinder will give you some more shots, but not the maximum possible unless you are at a site with 4500psi fills.
But by going bigger you lose any weight saving of fibre.
I would also say though that if using an Invert Mini and you are getting consumption at a level of 'gas hog' that something is wrong. (I've never fired a Mini in game so don't know how efficient they are, but 'gas hogs' should be things such as mechanical blow backs)
Look into other things such as adjusting velocity, paint matching etc and see if you can improve the efficiency