I get 8 moons for a similar setup. Although you might be able to play some tricks to increase this...
The number of moons the giant planet could have simply depends on how tightly they could be packed while maintaining orbital stability. Assuming prograde orbits, moons are stable out to about 1/2 of a planet's Hill radius RH, defined as RH = a (Mp/3Mst)^(1/3), where a is the orbital distance of the planet around the star, Mp and Mst are the planet and star masses.
Jupiter's Hill radius is about 0.35 Astronomical Units on its current orbit of 5.2 AU, so if it took the place of Earth, its hill radius would simply shrink by a factor of 5.2, down to about 0.07 AU. The orbital distance of Jupiter's outermost large moon, Callisto, is about 0.013 AU, so all 4 of Jupiter's big moons would still be stable if Jupiter were on Earth's orbit.
Now, how many more moons could we pack in if Jupiter were at 1 AU? Io's orbital distance is about 0.003 AU. LEt's assume that is the closest a big moon can form. The farthest is 0.07 AU, because beyond that moons would not be stable.
To make things simple, let's assume that the moons will be in a chain of orbital resonances (like the 4:2:1 Laplace resonance between Io, Europa and Ganymede). The total size of orbital space we have to work with is between 0.003 and 0.07 AU. <PERSON>'s 3rd law tells us that the orbital period scales as the orbital distance to the 1.5 power. 196
In orbital period space, we have (0.07/0.003)^1.5 = a factor of 112 in orbital period. Actually, to make the numbers work better let's move our inner edge inward a little to get a factor of 128. Now, let's assume that each pair of adjacent planets is locked in 2:1 orbital resonance, where the outer planet's orbit takes twice as long to complete. This would give us 8 moons orbiting the planet. The moons would make a resonant chain of (inner to outer) <IP_ADDRESS>. I've created similar resonant chains in computer simulations of planet formation and they are often stable. So, I think it's reasonable to assume this chain of 8 moons in resonance will be stable as well.
This is an analogous process to figuring out how many planets can be packed into a star's habitable zone. See here for more details on that: https://planetplanet.net/2014/05/21/building-the-ultimate-solar-system-part-3-choosing-the-planets-orbits/
And you may be able to sneak extra moons in on Trojan orbits. See here: https://planetplanet.net/2014/05/22/building-the-ultimate-solar-system-part-4-two-ninja-moves-moons-and-co-orbital-planets/ 196