You are essentially doing the same thing numerous JFBs have done in early 1942, just in reverse. The principle's the same, though. After you cross and shock (I highly doubt you take it first try against level 7 forts, but who knows) rest for a few turns to get your disruption and fatigue down. When both reach decent levels, then bombard the port with BBs (assuming you can get BBs there, considering mines, Japanese air, etc.) and order a deliberate attack. You will probably lose, but you will also probably lower the fort level one or two points if you have a significant AV disparity and combat engineers present. After this, simply rinse and repeat, until you lower the forts to level zero or one. At this point, rest your units a turn or two then order a shock attack - you'll most likely be the new owner of Singapore.
Note: This can be a lengthy process (honestly, it should be), but it works. If you are unable to run bombardment TFs in to help, then the process will be even slower, but it will still work.