I'm honestly not seeing a contradiction with the timeline that would set Ilberd up to be the Griffin. His funding takes a little more thought, but there's no contradiction with the time frame.

We first see the Griffin in the stinger of 3.1. Going by a very, very loose timeline, that's anywhere between 2 and 3 months after the ending of 2.55 and 3.1 at least. It was approximately 2 weeks to 2 months between the ending of 2.55 and 3.0, and 3.0 had to take place over the course of at least one tumultuous month. We dealt with Ilberd early on in the 3.0 story, meaning he was not in Lolorito's employ for 80% of it (and may well have not been in his employ for the entirety of 3.0, depending on when Lolorito kicked him to the curb). Add another month or so for the events of 3.2 and 3.3, and another month or two for the timeskip between Nidhogg's defeat and when we get to play again after the Ishgardian government reformation. So there's approximately 3.5 to 5 months between "Before the Fall" and "Soul Surrender;" plenty of time for Ilberd to get operations up and running as the Griffin.

The rest of the Masks don't look particularly well-equipped. The Griffin and his proxies do have some snazzy threads, but Ilberd was working for Lolorito - the wealthiest man in Eorzea - for some time. While certainly not loaded, he never seemed to be in want for coin (in fact Raubahn specifically called him out on betraying everyone for the Monetarists' coin), and with that getting some special clothes and rudimentary armaments for the Masks is far from implausible.

Both of the questions are pertinent if you're going to ask whether or not Gaius could be the Griffin. Time is not really a factor (2.0 end - 3.4 is a good length of time), but how the devil would a renegade Garlean legatus get the funds to supply the Masks in Eorzea of all places?

Gaius could be coaching Ilberd as the Griffin, but... I don't think that's plausible even. Aside from the whole "blown up in the Praetorium" thing, there would be too much of a clash in their personalities, and I can't think of a reason as to why Gaius would try to liberate Ala Mhigo. If I may be so blunt, the whole Gaius idea has felt like wishful thinking from the first...