This might suck, but i would say start with the furthest away...I've finished crunching through the data for all 8260 systems I got from EDSM and now have a list of 709 systems that contain gas giants with 8 or more moons, for a grand total of 863 gas giants.
The gas giant that's furthest away from the main star clocks in at a whopping 1,241,592 LS away. The medium distance for the 863 total gas giants on the list is only 1,501 LS, so the vast majority of those planets are reasonably close to the main star. Only 59 planets on the list are over 10,000 LS from the main star & 8 systems require a permit.
Elite Dangerous: The search for the Dark Wheel
The Dark Wheel System,Distance to Sol,No of Stars,Population,Permit,Gas giant,Distance,Checked Achelous,79,0.8409,4,651,0.234%,G V,1,9,549,219,250,Achelous 2,359 LTT 6278,81,0.5528,3,275,0.170%,M2 V,1,71,411,LTT 6278 1,325 LHS 3767,113,0.7943,4,687,0.167%,K3 V,2,32,735,LHS 3767 A 2,476 Dala,42,0...docs.google.com