As previous posters have said, just use standoff insulators. Which you'd want to do ANYhow. If you only need to gain another 1.5" clearance, I would suggest the easiest thing to do is use NAIL-ON insulators that you screw (not nail) onto pieces of 2x4 that you strap onto the outside of every other t-post. (edited to clarify: ideally they would be full height, so they are resting on the ground. You will get at least 5-10 yrs life out of them this way and they are real cheap to replace if you ever need to, so it is not something to sweat)
From the looks of it, that will do a perfectly satisfactory job.
At the same time, it is worth trying to tighten up the fence so it is STRONGER -- wibbliness is weakness. You don't need it professionally-installed, just do *yourself* what a pro would do
(although might have to wait for a less freezy season). First, you need proper corner posts (p/t 4x4 or cedar posts); t-posts
suck as corners and will always cause a saggy fence. Second, put in proper diagonal or h-style bracing on each side of each corner post, yes you can do this even if the run posts are t-posts. Third, release and retension the wire mesh (or use a crimping tool to retension it without having to release its attachments... but this does not work so well on 2x4 mesh and will shorten the lifespan of the galvanizing). That may be sufficient. If it's not, add a top rail (2x4 lumber is fine), and again, yes you can do this with t-posts you just have to be creative.
Good luck, have fun,
Pat