Best Jack to Change Tire on Single Axle Sport

OK, after 9 months of ownership, I have picked up a nail in a tire, creating a slow leak. 2014 Sport 22 FB, (single axle). Tire shops seem to not have the "proper" floor jack, and some just flat refuse to do the repair. One even went so far to tell me that "it was against the law to repair a trailer tire, it has to be replaced." I have to call "BS" on that one. So, I am relegated to going to storage, jacking up the trailer, remove tire, go get repair, reverse process.



Q: I have a 6 ton bottle jack. Is this an appropriate application, or is there is a better choice?



Thanks.