Bit for lunging?

[Stinkbomb]

Im wanting to start lunging Inky with a bit, having only used a caveson berfore. Hes bitted for longreining but Ive tried jointed snaffle, french link snaffle but inky doesnt seem to like them much so ive resigned to a mullen
Mouth snaffle.However i want to lunge him with a bit but think the mullen mouth might be alittle rigid for lunging?? Any ideas?
Please bear in mind he is only 32" so limited on bits i can use!!

 

[Miss L Toe]

Is he resistant to lunging in a headcollar under the bridle?.
To be honest I get the best result using two reins on the bridle, it is an extension of long reining, but you need to be nimble on your feet if he is not co-operative! and it takes a bit of practice as you have your hands full.
Make sure the bit is thin enough for a tiny mouth, this would be my main concern, I like happy mouth bits, but most are one thickness.