Most moving companies offer some version of a "pods" or container that's dropped off, picked up and delivered. So you may be better served reaching out to a few movers and see if they offer it. Good idea also to compare to "regular" moving services where they do the lifting and loading for you. In my experience, the cost difference hasn't been that much, at least for shorter moves. This article
https://threemovers.com/how-much-do-...st-for-moving/ has some info in regard to the costs, but you can get a more clear idea if you actually get a quote from movers (get a couple & compare).