Best bet is to pull out a tape and do some measuring on the rig and on the trailer. Wouldn't it just suck to have someone on the internet tell you things will fit fine and on moving day find out things don't fit at all?
If after measuring, I was not 100% certain things would work properly, I would do a test load before moving day. See if the trailer provider will let you hook up the trailer and test load the rig on it. This will verify the load and let you see better what kind of tie-downs you'll need.
Putting the smaller stock tires back on for the move will help. Among other things, you'll lower the center of gravity of the loaded trailer. This will help in the curves and cross winds more than you might think.
Keep in mind that free advice can frequently be worth less than you pay for it.