Your best option is indeed to farm Syrcus Tower for any ilvl 100 gear drops while also lotting on oils/sands that drop at the end, make sure you lot on all of them. Buy soldiery gear in Mor Dhona and unweather them to ilvl 110 with the sands (left side) and oils (right side). Everyone in the party will undoubtedly be lotting sands/oils though so they may be difficult to get.
Because of this, when you're around ilvl 100 I'd start looking into Second Coil of Bahamut. The lockout for it is gone as well and Turns 6, 7, and 8 are not very intensive for the main tank you just need to meet the accuracy cap which is 515 in Turn 9 (it increases for each turn but that is the highest you would need). You should be able to farm those much quicker than a Syrcus Tower run as most of the fights only take about 10 minutes to complete with a competent group. I would use that to push any holes in your gear set up to 110. You can find which items drop where here: https://docs.google.com/spreadsheets...#gid=884937690
Another change in the school of thought for tanking as well, depending on when you left, is that a lot of tanks will run with DPS accessories. I try to keep DPS accessories and tank accessories depending on the content. Turn 9 and the new Final Coil fights will probably be safer with tank accessories, anything else should be just fine with DPS accessories. All in all, I would not worry too much about getting the BiS items from the previous patches. As long as you can hit the acc cap for all turns, and the new turns, just focus on getting your ilvl to 110.
An additional thought in regards to your weapons, to get the unweathered 110 weapons you would need 1300 soldiery, an unidentified allagan tomestone, and a sands of time to unweather it. If you can get your other gear high enough that you can get into some of the new Shiva EX groups and learn that fight, she drops 110 weapons. This would probably be a much faster way to get the weapon as long as you can get decent enough gear in other slots to enter and win the fight.